But the Serie A giants face a battle to convince Liverpool to let him leave in a temporary deal.
The Reds would prefer a permanent transfer if they are going to lose the former Chelsea and Manchester City front man.
A £30m asking price is likely to scare off potential buyers but they would also demand a large loan fee.
Sturridge, 28, wants to leave Anfield to get regular first team football in a bid to salvage his hopes of making England’s World Cup squad this summer.
He recently returned to fitness but he has started just five games this season, scoring three goals.
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Liverpool are ready to listen to offers for the striker but will not let him leave on the cheap with 18 months left on his current contract.
Sturridge also earns up to £150,000-a-week in a heavily incentivised contract so any loan move would demand a big fee for the Reds hierarchy to consider.
Inter are ready to cover his wages and pay a loan fee and it remains to be seen if it will be enough to satisfy the Reds.
The England striker has found it difficult at the club since Jurgen Klopp took over in October 2015 and his injuries have only made it more challenging.
Sturridge has not played since Liverpool’s 7-0 win over Spartak Moscow on December 6 after sustaining a hamstring injury.
His five-year stint at Anfield has been blighted by calf, hamstring, thigh, ankle, foot and hip problems.