The Live News reports that the legendary Liverpool and England midfielder is ahead of Wayne Rooney and the current Saints boss Ruben Selles, who has struggled to turn the club’s fortunes around this season.
With just three games left to play, Southampton look to be relegated from the Premier League after an 11-year stay in the top flight.
Selles has odds of 9/1 to remain as manager next season, while Gerrard is the favourite at 5/1.
Read also: Could Arsenal Break Their Transfer Record Again This Summer?
Gerrard, who impressed in his first managerial role at Scottish giants Rangers, was sacked by Aston Villa earlier this season after a disappointing start.
Rooney, who has experience managing in the Championship with Derby County, is the second favourite to replace Selles with odds of 8/1.
Other former Premier League managers in the running include Jesse Marsch, Chris Wilder and Frank Lampard, with odds of 10/1, 12/1 and 16/1, respectively.
Southampton is expected to present a plan for dealing with relegation to the Championship, but replacing Selles could also be high on their agenda.
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