According to reports in Italy, Inter are hoping to land the Spaniard at the end of the season - when Barca could be tempted to sell.
The 30-year-old returned from a nine-month injury lay-off in August but new boss Tito Vilanova has used him sparingly since he came back.
Villa has started only one La Liga game all season and reports in Spain have indicated that he is not part of the Barca manager's long-term plans.
The striker's contract is up in June 2014 so he would command a fee next summer - but Italian paper Corriere dello Sport claim Inter are ready to stump up the funds.
That could force Liverpool into action, as they bid to reinforce their threadbare attacking unit.
Villas has been a long-term target for the Anfield club and he would certainly fit into Brendan Rodgers' style of play.