Prime Minister Theresa May has already committed to doing that, but many lawmakers don't trust the government and want an insurance policy.
That will be another key meeting - Macron was the major opponent to granting Britain a Brexit extension at last month's European Council summit, and he's expected to pursue a similarly hard line during Wednesday's discussions.
They also discussed upcoming European parliamentary elections with the PM saying that the government was working very hard to avoid the need for the United Kingdom to take part.
The French leader has taken the lead in pushing for the bloc to be ready to show Britain the door if Westminster can not not ratify a withdrawal deal. "This is why I believe we should also discuss an alternative, longer extension".
The UK wants the approval of all 27 European Union leaders to postpone Britain's departure until June 30, and for the UK to be able to leave sooner if parliament manages to ratify an divorce deal.
Germany thinks likewise. "There isn't an endless readiness to keep talking about delays so long as there is no substantial progress on the British side", said Michael Roth, Germany's deputy foreign minister.
"The prime minister's deal ... has a lot of the very positive attributes that anyone would want in a relationship where we can trade freely with the European Union".
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European Union leaders, worn out by the three-year Brexit crisis, have repeatedly refused to renegotiate the Withdrawal Agreement May agreed in November, though on Tuesday there was speculation in London that Merkel might be open to doing just that.
The majority of May's Conservative Party voted alongside the opposition Labour Party to back the prime minister's approach by 420 votes to 110. The preference in Europe is for a longer extension, either until the end of this year or until the end of March next year.
The EU has continually said it will not re-open the withdrawal agreement for negotiations, but Leader of the Commons Andrea Leadsom has renewed her plea for it to look at it again.
Meanwhile in London, talks will continue between Tory and Labour politicians with Labour pushing for a customs union, which the Tories oppose.
The debate was forced on the government by parliament passing a law on Monday giving lawmakers the power to scrutinise and even make legally binding changes to May's request to extend the Article 50 negotiating period.
If Britain's exit is delayed beyond May 22, the EU has said it will have to take part in European Parliament elections.
EU leaders at a European Council meeting in Brussels, Belgium, June 28, 2018.
He refused to suggest areas where the government could cross its red lines, such as on a customs union, in order to meet Labour's demands and stressed again that the government believed numerous benefits of a customs union were already outlined in May's proposals.