Cotterill, whose relationship with the Town supremo stems back almost two decades, said Wycherley is doing the responsible thing by deciding the next stage of the club's ownership.
The chairman celebrated 25 years at the helm this summer after buying the club in 1996 and, having turned 80, is believed to have been in talks to sell the club.
Cotterill, who was appointed at Montgomery Waters Meadow by Wycherley 11 months ago, said: "He's done a wonderful job and he's right to think about the future. What if he doesn't and something happens to him? God forbid.
"I think he's got some thoughts and ideas. And him having succession planning is the right thing to do, it has to be.
"Otherwise he's not a responsible owner, if he's not doing that. We see a lot of clubs at the moment in a lot of trouble because they haven't thought about succession planning, they just think about today and then what happens?
"One hundred per cent he will (leave it in good hands), otherwise he won't go anywhere just yet.
"Sometimes you don't actually know what you've got until it has gone. That's when people will look back on Roland's time.
"We could've bet the ranch, but we could go bust then. He won't bet the ranch, I know he won't! But he's alright – he's one of the good'uns still left."
Wycherley tried to appoint Cotterill from Cheltenham in the early 2000s. The boss turned down the move but met the Shrews chief and his board to offer advice.
The manager said: "What people see is him turning up in his Bentley on matchdays, someone said to me the other week he'd been getting a bit of stick for driving around in a Bentley or something, I told him to buy it!
"I won't be giving him any stick on it, I told him to go buy a new Bentley, because his old one was the old shape, so he's got the new shape.
"And you know what? If he wants to he can go and buy another one, and another one, one for every day of the week for all I care.
"I imagine at 80 you wake up and wonder how many years you'll be around.
"He deserves to enjoy his life, he's done everything for this club."