Liverpool are said to be prepared to sell Sturridge, provided their £30 million asking price is met.
And it is claimed that Stoke were 'ready to consider' a move for the 28-year-old, who reportedly earns £150,000 a week, but are now 'unwilling to make such a large investment' until they have a new manager in place.
Quique Sanchez Flores is the current front-runner to succeed Hughes at the Bet365 Stadium, and Stoke hope to have the Spaniard in place by Monday, according to the Sun.
18th-placed Stoke have averaged little more than a goal per game in the Premier League this season, and a fully fit Sturridge could help to address that shortage and steer the Potters away from the bottom three.
The England international has scored 75 goals in 194 top flight appearances, but has only played 431 minutes for Liverpool this season.
Would Sturridge be worth the £30 million investment for Stoke?