The 22-year-old has enjoyed a superb season with Monaco, who currently top Ligue 1 with a three point lead over Unai Emery’s side.
The midfielder is reportedly seen as a potential replacement for Michael Carrick at Old Trafford with the 35-year-old coming towards the end of a long and successful career with the Red Devils.
However, the Frenchman is not thinking about his future just now, although he admits he wants a move to a bigger club.
“I am very happy in Monaco. This club has brought me a lot,” he told Le Parisien. “I want to focus on this season. We'll see after. I hope that I will sign in a large club.”
Emery’s men could well invest heavily once again in the summer, particularly if they are pipped to the title by Monaco, and Bakayoko admits he would find it difficult to turn the capital club down.
"I was born and I lived all my youth in Paris," he added. "If the opportunity arises, I would not refuse to sign to the PSG. But I'm only 22 and I feel very good in Monaco."