Bolt said: “People think I am joking. But if Alex Ferguson called me up and said: 'OK let's do this, come and have a trial,' it would be impossible for me to say no. I would not take up the challenge if I didn't think I was good enough. I am a very accomplished player and know I could make a difference.
"I would be the fastest player in the team – but I can play as well. I am in Britain for a few more days. If Alex Ferguson wants to give me a call he knows where I am."
United's Rio Ferdinand tweeted Bolt: "If you want that trial at Man Utd shout me, I'll speak to the boss!! Well done in 100m." Bolt replied: "After the Olympics we work on that...lol..thanks man."
Bolt later told BBC 5 Live: "Rio's going to set the meeting up and I'm going to talk to [Sir Alex]."
More than 20m viewers tuned in to watch Bolt storm to victory in the 100m final on Sunday. He set a new Olympic record with his 9.63sec run and still has the 200m and the 4x100m relay to come.
A United spokesman told the Sun: "As the fastest man on Earth, he would undoubtedly add speed to the team."
The 6-foot-5 Jamaican first met United coach Alex Ferguson and the team when he visited Manchester in 2009 to take part in a 150-meter sprint through the city streets.