Betis, who are 11th in La Liga after 14 matches of the 2017-18 campaign, are believed to have funds to spend in the January transfer window.
Quique Setien's side have been strongly linked with a move for Arsenal midfielder Jack Wilshere, and it was claimed last month that the Seville outfit were confident of securing his signature on a free transfer next month.
According to El Gol Digital, the Spanish club are now considering a move for Sturridge, with the England international desperate for regular football in the second half of the season.
The 28-year-old has only scored three times in all competitions this term, and has started just five times in the Premier League.
A number of English clubs are also believed to be monitoring proceedings with the view to a January move.