The conversation was recently reignited when Gavin Bazunu joined the Saints in a £15m move from Manchester City.
The Republic of Ireland international spent the 2021-22 campaign on loan at Fratton Park, where he finished second in The News/SportsMail player of the season poll.
Bazunu will become the 55th player to play in both blue and red on the south coast.
But how many of those names have featured for Pompey and Southampton in the 21st century?
We’ve taken a look at the 13 players who have appeared for both clubs since the turn of the century.
9. Nigel Quashie
The central midfielder played a key role in Pompey’s title-winning campaign during the 2002-03 season. During his four-and-a-half year stay at Fratton Park, the former Scottish international made 181 appearances for the Blues before departing in 2005. Quashie still divides opinions after he joined Southampton in a £2.1m move from PO4 in January 2005. He joined Redknapp at St Mary’s but wasn’t successful in keeping the Saints in the Premier League that term. Photo: Mike Hewitt
10. Vincent Pericard
The Frenchman originally joined the Blues in 2002 on loan from Juventus, where he played a vital role upfront in the 2002-03 title winning campaign. He made his move permanent a year later but would only go on to make 13 more appearances in the two seasons that followed. While at Stoke, the striker spent two months on loan at Southampton but failed to score in any of his five games for the Reds. Photo: Craig Prentis
11. Matthew Robinson
The left-back came through the ranks at The Dell and would go on to make 17 appearances for the Saints. However, he would join Pompey in February 1998 and totalled 77 outings before he exited in January 2000. Photo: Chris Lobina
12. Dave Beasant
The famous FA Cup winning goalkeeper with Wimbledon joined Southampton in November 1993 and had a successful four year stay at The Dell, where he amassed 108 appearances between the sticks. The keeper joined Pompey in 2001 as Aaron Flahavon’s replacement following his tragic death in a car crash. Beasant made 28 appearances during the 2001-02 campaign. Photo: Craig Prentis