The 28-year old has stalled on making a decision though, fuelling speculation that he is not keen on a move to Italy.
Sturridge has not played for Liverpool since December and made only five starts in all competitions this season.
Having played for England just one in 2017, while also failing to make the most recent squad, Sturridge will be targeting first-team football in his attempt to make the plane to Russian Federation for the 2018 World Cup. Rafa Benitez is desperate to add more fire-power to his squad, but they have so far been frustrated in their bid for number one target Nicolai Joregnsen of Feyenoord.
Sturridge will wear the number 15 shirt at West Brom.
Meanwhile, Leicester do not want to allow forward Islam Slimani to leave on loan to another Premier League club, although Newcastle could be forced to put together a package which might appeal to the Foxes.