The Holland international has found himself frozen out of the first team at the San Siro following a dispute over his contract.
Inter are keen to slash their wage bill and, after selling Julio Cesar, Lucio and Maicon over the summer they have turned their attentions to Sneijder, who is their top earner with reported wages of €6million per season.
The 28-year-old, whose contract runs until 2015, has been told he will not play for the club until he agrees a wage cut.
However, with that outcome looking increasingly unlikely, a January move may be on the cards instead.
Big spending Anzhi Makhachkala were linked with a move for the former Real Madrid man earlier this month, though those rumours were swiftly denied by the player's agent.
Premier League duo Manchester City and Manchester United have also held a long-standing interest, while German giants Bayern Munich, Turkish outfit Fenerbahce and former club Ajax have also been linked.
Speaking to supporters outside the club's training ground Sneijder insisted that he was happy at the club but cast doubt on whether he would be staying much longer.
"I am happy here, but I don't know what will happen," the midfielder was reported as saying.
Meanwhile FIFPro, the professional footballers union, has expressed its concern at Sneijder's situation and a growing number of similar instances across Europe.
"FIFPro wants to talk to FIFA, UEFA and the European Commission about measures to adjust the behaviour of a growing number of clubs," read a statement.
"FIFPro signals a growing number of players who are put under pressure to prolong their contract. For clubs, football seems to have become more like business. Football comes in second place.
"'Clubs say that players must respect contracts, but why should that not apply in reverse? It is not as if Sneijder has taken a gun to the head of the board of Inter to force them to submit that contract. The club offered it to him with their full understanding.'"