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.
5. Eyal Berkovic
The ex-Israeli international started his career in England at Southampton in 1996, scoring four goals in 35 appearances during his 11 month stay at The Dell. He would later join Pompey in 2004 and became the Blues’ then highest paid player in the club’s history. He stayed for six months, scoring three goals in 28 outings before returning to his home country in January 2005. Photo: Tom Shaw
6. Scott Hiley
The right-back spent 18 months with the Saints before joining the Blues in December 1999. Hiley was awarded player of the season during his first full season at Fratton Park. In total, he amassed 80 appearances for the Blues before joining Exeter in September 2002. Photo: Getty Images
7. Ricardo Fuller
The ex-Jamaican international spent a season at Fratton Park on a pay-as-you-play deal following the earlier collapse of a £1.7m move from Preston earlier in the summer of 2004. The striker netted just one goal in 37 outings before making the switch to the Saints a year later. He fared much better in the Championship, scoring nine goals in 31 appearances for the Reds before departing in August 2006. Photo: Warren Little
8. Gregory Vignal
The former French youth international arrived on a two-year deal at Fratton Park from Liverpool in 2005. He spent just a season at PO4, featuring 18 times before returning to France 12 months later. The defender made a return to England in 2007, joining the Saints on a season-long loan, where he scored four goals in 23 outings. Photo: Stu Forster