The striker, who is currently out injured with a muscle strain, has struggled for regular action in Jurgen Klopp's side at Anfield, making just five starts in the Premier League this season.
The former Chelsea man has been fit for most of the campaign but has found himself behind Roberto Firmino, Sadio Mane, Mohamed Salah and even Dominic Solanke at times in the pecking order, and appears to have little realistic chance of regular action at the club again.
The 28-year-old has not given up on making Gareth Southgate's squad for the World Cup in Russia this summer, however, and knows he needs to play in the second half of the season in order to give himself a chance. Therefore, a loan move away this month looks likely and a switch to Inter has been mooted.
Tuttosport claim Sturridge has offered himself to Inter, where he believes he could flourish under Luciano Spalletti, who is on the lookout for another striker to help out Mauro Icardi.
Klopp is tipped to allow one of Sturridge or Danny Ings to leave temporarily this month and it appears Sturridge is the more likely, as things stand, as he is desperate to prove to Southgate he is worth considering for the Three Lions again.
Sturridge was part of England's Euro 2016 squad and has eight goals in 26 caps for his country, with his last appearance coming against Lithuania in August.