Sturridge is out of contract after leaving Liverpool at the end of the 2018-19 campaign, and according to a recent report, the 29-year-old has attracted interest from more than 13 clubs across the globe.
According to ESPN, there is strong interest, from DC United with the MLS club identifying Sturridge as a possible replacement for Rooney, who will be departing the club in December to join Derby County.
Rooney still has more than two years left to run on his contract at Audi Field but will be leaving to return to the English game in early 2020.
Sturridge, who has been capped on 26 occasions by England, left Liverpool having scored 67 times in 160 appearances for the reigning European champions in all competitions.
The forward has netted over 100 professional goals during a career which has seen him also represent the likes of Manchester City and Chelsea.