Sturridge’s future at Anfield remains unclear with the forward struggling to cement a spot in Jurgen Klopp’s starting XI.
Brazilian forward Roberto Firmino has instead led Liverpool’s front line for the majority of the season with Divock Origi offering further competition.
Despite retaining his place in the England squad, Sturridge is believed to be weighing up his options ahead of the January transfer window, with Stoke, West Ham and now AC Milan all registering their interest.
Reports from Italy claim Sturridge has been identified by Milan manager Vincenzo Montella as the ideal replacement for the misfiring Carlos Bacca in a deal that would be worth £25.5m.
Philippe Coutinho has also been linked with a move away from Anfield. Barcelona are allegedly interested in bringing the Brazilian to the Nou Camp and the club hope to use forward Neymar's close relationship with his international compatriot to help clinch the deal.
But Klopp has insisted that he isn’t worried about such rumours.
"It's about us, it's about the club," the German coach said. "The owners are not a problem so it's about creating the perspective that nobody wants to leave. If a club can pay double what we pay who am I to say to the player not to think of their kids or grandkids, but there are not a lot of clubs who can do this.
"I'm not worried about anything. The players like to be here. It's our job to keep it likes this. Very good players you always want to keep long-term. It's about creating a perspective where nobody wants to leave.
"My opinion is that he [Coutinho] feels very well here. We also hope and think his future is at Liverpool. He's still very young. You say now he's the player you've dreamed of. But he's now at an age where the skills and experience gives more consistently. With the team-mates he's getting better. It's only just started, it's not finished."