The 28-year-old is used largely in a back-up role by Reds boss Jurgen Klopp these days, being introduced from the bench in eight of his 12 appearances this term.
Sturridge has failed to even make it onto the field in Liverpool's last two games either side of the international break, however, despite netting two in two before that.
According to The Mirror, the former Manchester City and Chelsea ace now wants to leave Merseyside to revive his career elsewhere, having been cut from Gareth Southgate's latest England squad.
Southgate recently hinted that he only intends to take players playing regular football to the World Cup next summer, and the same report suggests that Liverpool are willing to listen to offers to help Sturridge's situation.
A loan deal may also be considered by both parties, although the Merseyside outfit are understood to have rejected a similar approach from Paris Saint-Germain last winter.