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.
13. John Beresford
Beresford arrived at Fratton Park in 1989 and would go on to play a key role in Pompey’s FA Cup semi-final run in 1992. During his three-year stay, he scored 10 goals in 132 appearances from defence before going on to have a successful career at Newcastle. The Saints would break their transfer record in 1998, signing the defender for £1.5m. However, the left-back only made 17 outings for the Reds before departing in 2001. Photo: Shaun Botterill