O’Neill is in the frame for the Northern Ireland vacancy but has yet to be interviewed by the IFA.
He has also been mentioned in reports in the North East of England relating to the managerial position at Hartlepool United after they parted company with Mick Wadsworth on Tuesday.
A former Newcastle United striker, O’Neill has served three years with the Hoops and has enjoyed unprecedented success with the revitalised club.
Second storm to hit Ireland after the weekend
Runners-up to Bohemians in his first season in Tallaght, Rovers have since won two League of Ireland titles and the Setanta Cup under O’Neill.
They have also made history as the first Irish team to make it through to the group stages of a European competition in the Europa League.
The visit of Spurs to Tallaght Stadium for the final Group A game on Thursday will now be O’Neill’s final game in charge of the Hoops.
“Michael will not be renewing his contract,” confirmed a source close to the 42-year-old Ulsterman last night.
“The club have offered him a two year deal but the board and Michael have different ideas as to where Rovers can go and about the potential of the club.
“Michael has no other job lined up but he will not be signing the new deal.”