The Scotland international played his first 90 minutes in the 2-1 win over Newcastle United after 11 months out with ulcerative colitis.
After advancing to the next round of the Capital One Cup, Cleverley told talkSPORT that he thought that Fletcher could make a difference to any team in the world.
"Fletch is a great player," said Cleverley.
"He's a big game player, he plays with high energy and he'd add things to any squad in the world. He's a great lad as well. It's fantastic to have him back."
United will face Chelsea in the fourth-round of the Capital One Cup.