The couple split last month following reports that the Wanted singer kissed another woman in a nightclub.
However, friends say that the pair still speak every day, sparking rumours of a reunion, The Mirror reports.
"Max and Chelle have chatted on the phone together every day this week, and it looks like things between them are improving dramatically," a friend said.
"He knows he made mistakes, but he still loves Michelle and wants to make another go of it. This is the first stage in rebuilding their relationship.
"Chelle has been upset by some of the things that have come out, but she still feels very strongly about Max too - she still loves him, and is seriously considering giving things another go.
"They're hoping to get together for a chat soon, but for now things are looking good in terms of getting their relationship back on track."
George had also been accused of having phone sex with an ex-girlfriend.
Keegan recently denied reports that she is dating Mark Wright.