Gazzetta dello Sport says Suning, Inter's owners, made contact with Messi earlier this year to register their interest. The approach was made well before the May 31 deadline of the expiry of a clause which allowed Messi to walk out on Barca for nothing this summer.
For the moment, Messi is committed to playing for Barca next season, but new contract talks remain ongoing. With less than a year left on his current deal, the Argentine can sign a pre-contract with Inter from January 1 before moving to Italy next summer.
It's also suggested Inter would be willing to better Messi's current €50m net salary by an extra €15m-a-year.
Suning believe a deal for Messi, no matter the cost, would pay it's way back by some margin through sponsors, a new stadium and merchandising.