The Israeli international could leave the Premiership club after contract talks broke down.
Abada has become the latest Celtic star to near the exit door after Georgios Giakoumakis joined Atlanta United in January.
The Hoops are prepared to listen to offers for the 21-year-old.
Talks over a pay rise for Abada have stalled and Celtic have failed to secure an agreement.
He could be on his way to the Premier League to join the Saints.
However, the south coast club must hold on to their top-flight status first.
Southampton are bottom of the Premier League after 28 games.
Only two points separate them from safety and manager Ruben Selles will hope to lead his team to survival.
They have scored just 23 goals, which is the second-lowest return in the league.
The attacking department is one the club will look to address, and Abada could be an answer to their woes.
He has notched 12 goals and four assists across all competitions for Celtic this term.
The former Maccabi Petah Tikva winger ended last term with 15 goals and eight assists.
No Southampton player has reached double figures in the league this term.
Bolstering their attack in the summer is pertinent, but whether Abada will be keen on joining them remains to be seen.
Even if they survive relegation, the Saints could be back in the battle for survival next term.
They spent the last two seasons fighting relegation, and Abada may prefer joining another club.
Last season’s PFA Scotland Young Player of the Year has won two Scottish League Cups with Celtic.
Ange Postecoglou’s side are a few games away from retaining their Scottish Premiership title.
Swapping such a team for one constantly fighting to avoid the drop makes no sense.
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