The English duo have progressed through the ranks at Old Trafford together since joining the club around the same time as youngsters.
Having committed his future to the Red Devils, Cleverley has tipped his compatriot to become a key player for both club and country.
"It was great to see Danny sign a new deal. It's a big boost for us," Cleverley told Inside United. "He's a fantastic player and someone the manager has great faith in.
"We've come up through the ranks together - we know each other so well and how each other plays and hopefully we can get some more game time together. We played some good stuff together last season but got injuries at different times and didn't get many chances to play together after the first few games. Hopefully that will change this season.
"Danny is a top-class striker and I think he can do big things for both United and England."
The pair have featured regularly for United so far this season.