Messi is currently sidelined at the Nou Camp with a knee ligament injury.
And with the Argentina superstar embroiled in an ongoing dispute with the Spanish authorities it is claimed he is considering leaving.
The Sun report Chelsea, Manchester United and Manchester City have all made informal approaches to Messi’s representatives this week – with one club making contact twice this week.
Messi was linked with the Prem’s big hitters in January but has apparently given indication he is willing to listen this time around.
The Sun add Messi often speaks to his friends who play in the Premier League such as Cesc Fabregas and Sergio Aguero.
A summer move is unlikely given the 28-year-old’s £180million release clause at Barcelona.
But in June 2017, Messi will be 30 with just a year left on his deal with the Spanish giants – making a move more feasible.
Messi and his father Jorge face trial over an alleged £3.1million tax fraud relating to image rights deals.
The man who wants to take the Messis to court is State Attorney Marta Silva Lapuerta, who intriguingly worked as secretary of the Real Madrid board under current president Florentino Perez.
However, Chelsea boss Jose Mourinho believes the Premier League lacks the pull to land a player like Messi.
“I think there are only three clubs in the world who have the power to say, ‘I don’t sell,’” Mourinho said in August. “This is Real Madrid, Barcelona and Bayern Munich.
“Is anyone in England interested in Thomas Muller? For sure. Can we, England, bring Thomas Muller from Bayern? I don’t think so.
“Does anyone want [Lionel] Messi? Can you bring him? I don’t think so. They are big clubs with big history, economically strong and stable, income amazing. I think they sell when they want to sell.
“When you see a player leave one of these big clubs you have to think it’s because they want him to go. That’s my feeling.
“[I’m] speaking about the ones who make the world stop. Big transfers. When does Messi leave Barcelona? When he finishes his career.”