The Liga side are the England international’s first-choice option, but have only put in a check over his availability.
Inter, however, have submitted a “serious” proposal to sign the 28-year-old until the end of the season, which includes a substantial loan fee, the full assumption of his salary and a path to making the deal permanent.
The Serie A outfit have made it quite clear in their professional handling of matters that they are resolute in securing Sturridge’s services, which has encouraged the forward.
Sevilla’s interest in Sturridge is further complicated by their pursuit of Michy Batshuayi from Chelsea .
The 24-year-old had seemed certain to switch to the Ramon Sanchez Pizjuan for the rest of the campaign, but the London club’s difficulty in the transfer market is hampering that move.
But the West Ham target man has suffered an ankle injury, which has left Chelsea scrambling and Sevilla frustrated.
Vincenzo Montella’s side, who have conceded more than they have scored in La Liga this season, are now considering making an official submission to Liverpool for Sturridge’s services.
They have been made aware it would need to match what Inter have put on the table.
Sturridge, who has previously revealed his fascination with Spanish and the intention to increase his vocabulary in the language, was an unused substitute during the 3-3 Champions League draw at Sevilla in November.
He has been handed just five starts for Liverpool this season, and following a muscle issue, as well as illness which he has shaken off, he has not featured in a matchday squad since the 7-0 victory over Spartak Moscow on December 6.
Liverpool were initially unwilling to countenance a loan move for Sturridge, placing a £30 million valuation on the marksman.
However, having only received approaches over a temporary arrangement thus far, the Merseysiders are looking to settle on the best deal for the club and player before the window closes.