The 25-year-old enjoyed a successful 2021-22 campaign with the Gers, recording nine goals and 10 assists in 57 appearances across all competitions, including a strike in the Europa League final defeat against Eintracht Frankfurt.
According to journalist David Ornstein of The Athletic, the Saints face competition from another unnamed club for Aribo's signature, but they are confident of completing a deal to sign the midfielder, who is keen to move to the Premier League and join Ralph Hasenhuttl's side this summer.
Ornstein adds that a four-year contract is being lined up by Southampton for the Nigeria international, who has a £10m release clause in his Rangers contract.
The former Charlton man is currently in London and it remains to be seen whether he will join up with the rest of the Rangers squad on Thursday for their pre-season tour in Portugal.
Aribo, who has just 12 months remaining on his contract at Ibrox, could become Southampton's fourth signing of the summer window after Gavin Bazunu, Mateusz Lis and Armel Bella-Kotchap. body check tags ::