Saints boss Nigel Adkins has moved to bolster his squad for the promotion run-in as Morgan Schneiderlin is currently sidelined with a knee injury while Adam Lallana and Alex Chamberlain picked up knocks in midweek.
Stephens, 21, has made 37 appearances for the Latics this term, scoring 10 goals, and his performances have reportedly attracted interest from Leeds as well as some Premier League clubs.
Oldham turned down an offer from Saints earlier this week but the player has since decided on a move to the south coast.
Manager Paul Dickov told his club's official website: "When Southampton came in we turned down their offer and Dale told us he wanted to stay. But after speaking to his agent he came back and expressed a wish to speak to them."
Source: PA
Source: PA