Mr Tusk, the president of the European Council, said he will "appeal" to the heads of the other 27 Union states to consider the matter.
Writing on Twitter, he said: "I will appeal to the EU27 to be open to a long extension if the UK finds it necessary to rethink its Brexit strategy and build consensus around it."
This comes after the Commons voted in favour of ruling out no-deal in any circumstance.
Both British politicians and EU figureheads have previously stated an extension to the deadline, currently set at March 29, might be necessary.
After voting in favour of ruling out no deal, MPs will have their say on Thursday on whether Theresa May can ask the EU for the date to be moved back.
This is a decision Britain can not take alone and the EU27 will have to approve the idea.
The Prime Minister's motion says if the House of Commons has approved her Withdrawal Agreement and the framework for the future UK/EU relationship by March 20, she will seek a one-off extension.
This would be requested to be until June 30 to allow time for the necessary legislation to be passed.
Should her deal again fail to win Commons support, the motion warns it is "highly likely" the EU will require the UK to set out a "clear purpose" before granting any extension.
It adds that any delay beyond June 30 will involve Britain taking part in May's elections to the European Parliament.
Mrs May has previously said she hoped any delay to Brexit and extension to Article 50 would be short.
Chancellor Philip Hammond has said it is "certain" MPs will vote to authorise Theresa May to seek a delay to Brexit.
He denied being at odds with the Prime Minister after calling for Parliament to seek a "consensus" solution to Brexit and to "explore other options" if her deal is voted down for a third time next week.
Prior to the comment from Mr Tusk, multiple EU leaders stated their stance against an Article 50 extension unless there was a clear mandate of what Parliament hoped one would achieve.
The bloc's chief Brexit negotiator, Michel Barnier, said: "They have to tell us what it is they want for our future relations, what will their choice be?
"What is the clear line they will take? That is the question we need an answer to.
"Why would we extend these discussions because the discussion on Article 50 that is done and dusted, we have the withdrawal agreement and that is there."
While another EU Brexit negotiator, Guy Verhofstadt also called for clarification from the Commons.
Speaking to Sky, he said: "I don't see any reason to give any extension if first of all we don't know the majority position of the House of Commons.
"Why we should start to give even a short extension if there's no clear position of the House of Commons."
Brexiteer MEP Nigel Farage called on the bloc to "veto" an extension as he spoke of his desire to leave during a speech in Strasbourg on Thursday.