Former Wales Under-21 boss Brian Flynn, who has been working for Rovers as a scout, and captain Rob Jones have been placed in temporary charge of first-team affairs while the south Yorkshire club conduct their search for a new manager.
Saunders left Doncaster on Monday after almost 16 months in charge to take over at Championship strugglers Wolves, who sacked Stale Solbakken on Saturday evening following their FA Cup third-round defeat at non-league Luton.
A spokesman for the club said: "The board have met and will now invite applications, but the club are in no rush to make an appointment.
"It is important that we get the right man who will enable us to continue our promotion push.
"Brian Flynn and captain Rob Jones will take charge of the team for Saturday's game at Stevenage, with the club aiming to have a new manager in place in time for the next home game against Leyton Orient."
Saunders' final game in charge, Saturday's 1-0 win over Colchester at the Keepmoat Stadium, saw Doncaster move level on points with Tranmere at the top of the League One table.