On Thursday, Mr Johnson denied he was holding up the report. The Cabinet Office is keen to ensure none of its contents undermine the Metropolitan Police’s new probe into the matter.
MPs across the political spectrum are not expecting the report to be published before Monday, given many have left London for their constituencies for the week.
But Ms Gray has the power to decide herself when to hand her report to Mr Johnson, meaning uncertainty remains about the exact timing.
For weeks, the Prime Minister has been considering how to announce an overhaul of No 10’s culture and staffing in the wake of Ms Gray’s report.
But supporters who have discussed the situation with Mr Johnson in recent weeks have told The Telegraph they fear his “reset” plans do not go far enough.
“It is all going to depend on his reaction. I still think that is the big issue,” said one source.
“If he is contrite, if he moves the agenda on, if he changes people – I think those are things that will make a difference.
“If he doesn’t do that, then I think the letters will rush in. This can’t go on, this has to be a big reset.”
A second source said: “We need to do a major reset to get through the May elections. I’m worried that what is coming is not enough.”
Plans to announce changes to Mr Johnson’s closest advisers and aides have been complicated by the launch of a police investigation into the alleged parties.