Ahead of the Brussels gathering, which Mr Johnson will attend, French President Emmanuel Macron and German Chancellor Angela Merkel will meet in Toulouse.
If a Brexit deal is approved by EU leaders at this week’s summit, the House of Commons could be asked to approve an agreement in a rare Saturday sitting.
However, Mr Barclay told the committee he could not yet confirm whether MPs will be asked to be in Westminster this weekend.
Mr Johnson held a “constructive” telephone call with Irish prime minister Leo Varadkar this morning, Downing Street revealed.
The prime minister’s spokesman said “progress was made” on a Brexit deal “but there is still work to do”.
A cabinet meeting scheduled for 4pm has been brought forward to 2.30pm, Number 10 added.
An email has also been sent to Conservative MPs informing them that Mr Johnson will now address them at a gathering of the 1922 Committee at 4.30pm, instead of 7.30pm.
The group of all backbench Conservative MPs, chaired by Sir Graham Brady, is responsible for Tory leadership elections and their meetings usually provide an indicator of support for the leadership, direction of the party or major policies.