The Sun is of the belief that Chelsea has emerged as a genuine candidate to sign the Argentine ace if he happens to leave Barcelona.
Blues owner Roman Abramovich has reportedly met with Messi's father and agent, Jorge, on his yacht within the last 10 days.
Messi has been sentenced to 21 months in prison for tax fraud - although he will unlikely serve any time behind bars - and during the case, it is understood that Barcelona failed to support him as strongly as they could have.
There are murmurings that Messi is unhappy with the lack of support and the fact Barca are yet to offer him a new contract has also weighed on his mind.
Abramovich took the time to meet with Messi Snr in a bid to put the West Londoners in pole position if the 29-year-old were to end his 15-year association with the Catalan giants.
Manchester City, managed by Pep Guardiola, are also keen on Messi but the report from The Sun suggests that Chelsea are making their presence felt just in case a Camp Nou departure becomes a likelihood.