The Barcelona superstar is yet to agree a new deal with the Spanish champions and as things stand will be available on a free next summer.
Messi has played his whole professional career at the Nou Camp and has always insisted that he is happy to stay with the Catalans until he retires.
But for the first time there have been noises coming out of Barcelona that the Argentine could finally decide to try somewhere new.
There have been several off-the-field problems at the club in the last year, while the team are not what they were previously.
Indeed, Messi and co relinquished their La Liga title to Real Madrid last season after an out of the ordinary campaign.
And, according to Italian outlet La Gazetta Dello Sport, Inter are ready to offer Messi a humungous package to try to sign him up.
The report claims the Nerazzurri are willing to hand the 33-year-old £60million a season and would offer him a four year deal.
With a collective salary of £235m over the length of that contract, Messi would earn more than Cristiano Ronaldo does at Juventus.
Ronaldo was making £27.3m from his salary at Juve, before any coronavirus-related pay cuts.
Moving would of course see the old rivals reunited for the first time since Cristiano left Real Madrid for Turin in 2018.
Just days ago Inter's owners hinted at a summer move for Messi by using his picture to advertise a Serie A game in China.
Both Inter and Chinese streaming service PPTV are owned by the Suning group.
And they projected a picture of Messi on Milan’s Duomo cathedral to advertise the Serie A game between Inter and Napoli for their Far East audience.
Speaking after Barcelona’s disappointing loss at home to Osasuna at the end of last season, Messi criticised his Barcelona team for dropping their standards.
Messi spoke about other sides bettering them for intensity, claiming: “This result summed up what we have been all season, a very inconsistent team”.