It is understood the Magpies have made contact over the 28-year-old, but that discussions are still at an early stage and his wages could prove a significant obstacle.
There are a number of clubs both at home and abroad interested in the England international with Newcastle by no means having a free run.
Feyenoord's Nicolai Jorgensen is another target but negotiations appear to have hit an impasse over the two clubs' respective valuations of the player.
Sturridge has made only 14 appearances for Liverpool and has scored three goals to date this season.
Last Friday, Jürgen Klopp warned the player that he cannot promise him playing time in the coming months if he decides to stay.
“I have never in my life promised a player game time for the next few months,” Klopp said. “It is not possible. We have mentioned all the things like it was so far.
“When Daniel is fit, training in shape he is still an outstanding striker there is no doubt about that. But he did not play the last few weeks – for different reasons.
“Of course one of them was Roberto Firmino's performance, then Dom Solanke's development. And Daniel was in and out of training. In general more in than out in training, but the time he was in he was a little unlucky with games. That was the situation, not more.”
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