The Daily Mail says Wilder is keen on snapping up free agent Sturridge following his release from Turkish side Trabzanspor earlier this year.
His contract with was ripped up in March after he was hit with a four-month ban for breaching betting rules.
But Sturridge has been training hard to keep himself fit.
And despite being linked with David Beckham's Inter Miami, the English hitman has his sights set on another shot in the Premier League.
Sheffield Utd are eager to strengthen their forward line before next month's transfer deadline.
And a deal securing Sturridge until the end of the season is starting to look like a real possibility.