Stoke sacked Alex Neil last week and are closing in on the appointment of Schumacher as their new manager.
The 39-year-old got Plymouth promoted to the Championship and was doing well with them before Stoke came in and worked out compensation for him.
The appointment is expected to be confirmed soon but Clarke feels Schumacher is making a mistake by agreeing to become the next Stoke boss.
He feels there is something seriously wrong behind the scenes and several good managers have failed to get them going in recent years.
The former EFL star pointed out that Stoke have made no progress despite spending top money on some good managers at Championship level.
Clarke said on the What The EFL Podcast: “I wouldn’t do it if I was Schumacher.
“A lot of good managers have gone there and done nothing; I think there is something rotten behind the scenes.
“I don’t know enough about Stoke City and the way the club are run to really comment but they have just not made any strides.
“They have not got a philosophy, they have sort of bumbled around for a number of years, paid a lot of good money for good managers but they have been unable to get consistent results.
“I would want to do my homework on the people I was working with Stoke before jumping ship.”
Stoke snared Neil away from Sunderland last year but more than a year later he was moved on with them sitting 19th in the league table.
