There was speculation that Pardew would lose his job at the end of last season but the 49-year-old remained in charge and strengthened his squad in the summer, signing the likes of Ryan Dickson, Frazer Richardson and Danny Butterfield.
Southampton lost their opening game of the current season, at home against Plymouth, drew their second league fixture and thrashed Rovers on Saturday.
They also defeated Bournemouth in the Carling Cup before losing to Premier League Bolton 1-0 in the second round.
Pardew is the fourth Football League manager to leave his club this season, after Steve Coppell at Bristol City, Kevin Blackwell at Sheffield United and Chris Turner at Hartlepool.
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