The injury-prone striker has been heavily linked with moves to Newcastle, West Ham and Stoke in recent weeks.
Liverpool have reportedly placed a £30m price tag on Sturridge.
And the forward will be keen to play regular football ahead of the World Cup later this year.
But speaking today, Klopp would not be drawn on the Liverpool star's future.
"I have nothing to say about that," he said.
"Until January 31, a lot of things can happen.
"We will see, not just with Daniel, with everything.
Daniel Sturridge next club: Latest odds

“He is back in training and is on his way to being fit”
Jurgen Klopp
"He is back in training and is on his way to being fit."
Klopp was more comfortable offering an injury update for his side.
While Sturridge is returning to full fitness, others are closer to a first-team return.
"Henderson is out on the pitch and looks good," he added.
Getty
Getty
"Moreno trained yesterday and should be ready after Sunday.
"If nothing happens, he still needs time to train."
Klopp also announced Mohamed Salah was back for the visit of Manchester City this weekend.