The Northern Irish tactician has come under growing pressure after a five-match winless Liverpool run in all competitions.
But Toure, who spent several seasons under Wenger at Arsenal, backed Rodgers to get his side back into form.
"I do see Wenger in him because he's so intelligent," Toure said.
"He knows how to speak to players and how to get the best out of them. He will prove that because we will come out of this hard time.
"Like Arsene, he's always there at training trying to improve things. His style of play is also similar. He always wants us to pass the ball and keep playing which is very important."
Toure is certain Liverpool, who are 12th in the Premier League and battling in Europe, will return to form.
The 33-year-old Ivorian said Rodgers needed time, particularly in the UEFA Champions League.
"He's right up there [with the best]," Toure said.
"He's young as a manager. This is the first time he has managed in the Champions League.
"He is learning. The Champions League is tough. We've seen it with teams like City, who have found it tough. You have to learn about it.
"You need time as a manager. I think he has done a great job for this club and we like him. He works so hard and gives 100 per cent. That’s why I am sure we will get out of this spell we're in."
Liverpool host Stoke City on Saturday.
