The 19-year-old has been strongly linked with a move to Bundesliga side Bayer Leverkusen for much of the summer transfer window in a deal worth a reported £5m.
According to the Daily Mail, Southampton are now looking to acquire Edozie’s services before a move to Germany finalises.
Manchester City boss Pep Guardiola handed Edozie his full Citizens debut in last summer’s Community Shield game against Leicester City, but he hasn’t made an appearance for the first team since.
Edozie trains with City’s Under 23s squad and is a regular in Premier League 2, scoring five goals in 27 games over the past two seasons.
Saints have already signed two Manchester City prospects in the summer transfer window in Gavin Bazunu and Romeo Lavia.
Southampton have also been linked with signing promising striker Liam Delap from City over the past few days, with a transfer bid reportedly rejected.
Former City recruiter Joe Shields has recently joined Southampton as head of senior recruitment which could see Saints linked to - and signing - more talent from the blue side of Manchester.