The Mail on Sunday says Saunders is the man Wolves want to replace Stale Solbakken.
Doncaster Rovers will be approached by Molineux owner Steve Morgan in the next 24 hours for permission to speak to the former Wales international.
Saunders has been recommended to Morgan via his connections in Liverpool.
The multi-millionaire, who counts luxury hotel Carden Park among his business interests, is believed to have already sounded out contacts at Wrexham as he started due diligence into the ex-Wales assistant boss.
Saunders, 48, was in charge of Doncaster when they were relegated from the Championship last season.
However, he has maintained steady progress following the club's demotion and they are among the frontrunners for promotion from League One.