Donny sacked Gary McSheffrey as manager on Monday morning following a disappointing campaign so far in League Two and are now looking for his replacement.
A run of just seven points from eight games was enough for Doncaster to pull the trigger on McSheffrey.
Doncaster are now looking toward former Huddersfield boss Schofield, with his name spoken of within the corridors at the club.
Schofield was sacked by the Championship club earlier this season after they failed to start the season well.
It is suggested that he could be tempted by the prospect of taking charge of Doncaster.
Donny were beaten 3-0 away at Carlisle United on Saturday and have lost three of their last four matches.
They are next in action at Crewe Alexandra and it remains to be seen if Schofield will be at the helm when they step onto the pitch at Gresty Road.
