The England international has been made available by the Reds this month, with Newcastle and Sevilla making enquiries.
The Liverpool Echo says Inter are also keen on him.
While Liverpool are prepared to off-load Sturridge during the current transfer window they apparently favour a permanent deal.
Inter insist they aren't in a position to match the Reds' £30million asking price.
But they would be willing to pay a loan fee and all of his wages.