The Sun has claimed that Manchester City, Manchester United and Chelsea have contacted Messi's representatives regarding a transfer from Barcelona.
The 28 year-old Argentine star has been in Catalonia for 14 years, and it is claimed that he would enjoy the opportunity to test himself in the Premier League.
His interest in moving could also be motivated by the recent tax fraud investigation brought against him and his father. Messi and his father are facing trial over an alleged £3.1 million tax fraud.
Currently, the four-time World Player of the Year is on the sidelines due to a knee ligament injury. He said: "I am improving every day without setting myself any targets. I have always said that I don't set myself any dates because it isn't up to me.
"As much as I would like to play tomorrow, the doctors wouldn't let me. When they tell me that I have recovered completely will be the time that I will make my return onto the pitch."