Cleverley says the constant competition is part of life at United.
"It is always going to happen at a club like United that new big names will be linked," he told the Manchester Evening News.
"But no matter the names mentioned this summer, they don't come bigger or better than Paul Scholes. I already have the hardest job in the world to get past him.
"Add to that Michael Carrick, who is one of the best in the country, and it is a tough time ahead. But it is a challenge and all part of the learning process. You can't get too frustrated when you are still learning from the best in the world."