The 22-year-old is being lined up as Saints' number one target for the summer, according to reports.
The 22-year-old came through the youth ranks at St Mary's before departing for the Emirates in 2011. However, his time with the Gunners has failed to properly ignite, leaving his former club pinpointing the England international as their number one target for the summer, according to the Mirror.
And Le Tissier has suggested that rejoining Ronald Koeman's side may be the right thing to do after a frustrating spell in north London.
"He's a very good player," he told the Mirror. "He’s obviously suffered with injuries in the last couple of seasons so he's not really been a regular in that Arsenal side.
"If the boy wants to play regular first team football and be a first choice in the team then sure it’s realistic, it’s not like he’d be dropping down to the bottom half of the table.
"He could join a team that are challenging for European places. OK, it's not the Champions League at the moment but we've certainly challenged for Europa League places over the past three seasons."
Although injuries have played a significant part in Oxlade-Chamberlain's time with Arsenal, he has not really been able to progress even when he has been fit.
Arsene Wenger's squad boasts a cluster of fantastically-gifted wingers and attacking midfielders, which has meant that only nine of the youngster's 22 Premier League appearances this season have seen him in the starting line-up.
As Le Tissier suggests, a move to the Saints would not be a huge step backwards considering that he will be able to become a focal point of a side that has proved in the last couple of seasons that qualifying for Europe is certainly not beyond them.