The Daily Mail says the former Newcastle and West Ham captain has been asked by Orient owner Francesco Becchetti to step down. But Nolan will refuse.
And that disagreement will see the 33-year-old quit the League Two club after just 15 games in charge, even with a place in the play-offs still a possibility.
Becchetti wants to be able to communicate with his fellow Italian countrymen in the dugout from the stands as he seeks to gain more influence over matches.
Orient lost 3-0 at Barnet on Saturday in the latest game in a run of four without a win which has seen their hopes of immediate promotion back to League One fade.