The Spain international has struggled to find consistency since moving to Stamford Bridge for £50m in January 2011, scoring just nineteen goals in one hundred and nine Premier League appearances.
Reports in Italy are suggesting that Inter will initially attempt to take the 30 year old on loan before completing a £10m bid next summer.
The former Liverpool striker has also been linked with a return to his first club Atletico Madrid, who is faced is the semi-finals of the Champions League last month.
During his time with the Blues, he has won the FA Cup, Europa League and the Champions League, and was also victorious in the 2012 European Championships with Spain, where he finished the tournament as top scorer.
However, there are doubts whether he will be selected to help his country retain the World Cup in Brazil this summer.