Donald Franciszek Tusk is a Polish politician who has been the President of the European Council since 2014. He served as Prime Minister of Poland from 2007 to 2014 and was a co-founder and chairman of the Civic Platform political party.
The Meeting comes after MPs rejected the PM's plan to fast-track a bill to implement his deal through Parliament.
During PMQs, Mr Johnson said MPs had "willed the end But not the means" and it was now the EU's decision whether to grant an extension beyond 31 October.
Labour was keen to discuss a different timetable for the Brexit bill, while the PM wanted to know what Mr Corbyn would do if the EU refused to grant an extension, she added.
A Labour Party spokesperson said: "Jeremy Corbyn reiterated Labour's offer to the Prime Minister to agree a reasonable timetable to debate, scrutinise and amend the Withdrawal Agreement Bill, and restated that Labour will support a general election when The Threat of a no-deal crash-out is off the Table . "
No 10 said there had been "no meeting of minds" between the two men and no further talks were currently planned.
The PM announced that he would pause the progress of the Withdrawal Agreement Bill (WAB) on Tuesday after MPs rejected a plan to pass it in just Three Days .
EU leaders, meanwhile, are considering whether to grant a delay to the Brexit deadline and what length it should be.
Laura Kuenssberg said a decision was not expected until Friday, leaving Westminster "still in limbo".
Mr Johnson was forced by law to send a letter to Brussels requesting a three-month extension, and No 10 had indicated he would push for a general election if the EU agreed.
In the meantime, President Tusk's consultations with EU leaders will continue.Analysis: BBC Europe correspondent Kevin Connolly
The EU is in no hurry to settle its attitude towards another Brexit extension because it's under no immediate pressure of Time - the current extension runs until midnight on 31 October. The instinct of the European Council is to take the Time it needs to reach agreement, even if that's seen as frustrating in Downing Street.
Donald Tusk as President of The Council acts as a kind of convener for the 27 heads of Government - each has to be consulted at least once by phone so The Process takes a little Time even when The Matter is straightforward.
The Council works by unanimity so whatever it eventually decides will have to be acceptable to all 27 and it's true that there are differences of emphasis - there's a view In Paris , for example, that a shorter extension might concentrate minds in London.
The EU has its own limits to consider as well. First, it doesn't want to look as though it's pressuring Parliament into any particular course of action.
Second, it's clear the EU will never want to look as though it's forcing the UK out of the Brexit door or be The Cause of a no-deal Brexit - for that reason, whatever the frustrations, an offer will come.
At Prime Minister 's Questions, Mr Johnson said it was "remarkable" that MPs backed the Withdrawal Agreement Bill at its first Commons hurdle, But a "great shame" that MPs did not back his proposed timetable for it.
He said it was "peculiar" that Mr Corbyn appeared to want him to bring back The Bill when Labour MPs were told to vote against it on Tuesday.
In reply, the Labour leader said it was Mr Johnson who had "decided to delay his own withdrawal bill" when he made the decision to pause it.
Mr Corbyn also accused Mr Johnson of trying "to prevent genuine democratic scrutiny and debate", adding: "Does the Prime Minister accept that Parliament should have the necessary Time to improve on this worse-than-terrible treaty?"
Detailed dissection by MPs at The Committee stage would come next - along with attempts to amend The Bill - followed by further votes in The House . If it was eventually approved by The Commons a similar process of scrutiny would be carried out by peers in The Lords .
The SNP has indicated it wants an extension to allow for a general election, while the Liberal Democrats say the PM needs to get an extension to allow a further referendum. Both parties would rather the UK revoked Article 50 and stopped the Brexit process.
But Mr Johnson said the Scottish Parliament had no role in approving the Brexit bill and suggested Mr Blackford "have a word with other opposition parties" to trigger a general election "to settle The Matter ".
In a statement responding to Mr Johnson's and Mr Corbyn's earlier meeting, Ms Swinson said it was "more clear proof" that the Labour leader wanted to deliver Brexit , after 19 Labour MPs supported The Bill 's second Reading .
Under the Fixed-term Parliaments Act, the Prime Minister needs to have the backing of two-thirds of MPs to hold a snap poll. This has been rejected twice by MPs.
Another route to an election is a one-line bill, that requires only a simple majority, But any such bill is likely to incur a host of amendments, for example, giving 16 and 17-year-olds The Right to vote.
There is also the option of a vote of no confidence in the Government , and Mr Johnson could even call one himself.
But Parliamentary rules state that if it passes, The Commons has 14 days to form an alternative administration, so the PM would run The Risk of being forced out of Downing Street if opposition parties can unite around a different leader.
If an election were to be triggered This Week , the earliest it could take place would be Thursday 28 November, as The Law requires 25 days between an election being called in Parliament and polling day.
The fact that talks took place between Jeremy Corbyn and Boris Johnson suggests that No 10 may not be totally wedded to the idea of a winter general election. Pressed in The Commons the PM did not close the door to bringing back his deal.
And there are those in Government who are deeply wary of a winter election. Why? Bluntly, because it is so blooming cold.
No-one is going to thank him if they have to tramp off to The Polling station in the bleak midwinter. There's a fear that older voters would be The Most likely not to turn up - yet those may be The Ones who were keenest to back Brexit .
Then there is The Nativity play problem. Many school halls, which are used for polling stations, have been booked up for Christmas Activities - and woe betide Mr Johnson if he forces those to be cancelled.