The European champions lie sixth in Serie A after Sunday's defeat by minnows Chievo and have now gone four games without a win, prompting speculation that Inter president Massimo Moratti is searching for a new coach, says the Daily Mail.
Capello - who Inter tried to prise from the FA before the World Cup - is said to top that list, with Leonardo, Diego Simeone and Zenit St Petersburg coach Luciano Spalletti also being considered.
The FA h ad to renegotiate Capello's contract when Inter came calling in the summer but the Italian has since overseen a dire World Cup and a dismal display against France last week.
An approach by Inter could also suit the FA financially. Capello would have received £6million if fired, but if he chose to leave the FA would be paid a seven-figure sum in compensation.