The 24-year-old burst onto the scene with Real Valladolid before making the move to St Mary's in 2020, but he could not prevent the Saints from dropping down to the Championship for the 2023-24 campaign.
As a result, Salisu is one of several Saints players expected to depart in the coming weeks, as his contract is only due to run until the end of the upcoming season.
According to The Athletic, the Ghana international is now on the brink of a summer switch to Monaco, who have now had a bid accepted by Southampton after agreeing personal terms with Salisu.
The defender was previously linked with a £15m switch to Fulham, but the Cottagers instead turned their attention to Calvin Bassey, giving Monaco a clear run at his signature.
Salisu is expected to complete his medical with Les Monegasques early next week, and he departs Southampton with a record of one goal and one assist from 80 matches in all tournaments.
In addition to Salisu, James Ward-Prowse is also in the St Mary's departure lounge, and West Ham United are believed to be preparing an improved offer for the Saints captain.
Ward-Prowse has apparently been the subject of one failed £20m bid from West Ham, who offered Southampton an upfront fee of £17m with an additional £3m in add-ons.
Unlike Salisu, Ward-Prowse's contract on the South Coast still runs for another three years, allowing Southampton to play hardball in negotiations over their skipper.
Now, Football Insider claims that West Ham are ready to up their bid to £25m, and Ward-Prowse would be open to a move to the London Stadium in order to remain in the Premier League.
However, Southampton are believed to have slapped a £40m asking price on the head of the 28-year-old, who has been on the books with the Saints for 20 years since joining their youth setup in 2003.
Ward-Prowse has since registered 55 goals and 53 assists in 409 appearances for the senior Saints team, and he could arrive at West Ham as a replacement for £105m Arsenal signing Declan Rice.
Elsewhere in the Premier League, Newcastle United and Everton are apparently ready to go head-to-head for the signature of Red Bull Salzburg centre-back Oumar Solet.
The 23-year-old has gone from strength to strength in Austria since leaving Lyon in 2020, winning three successive top-flight titles and representing his side in the Champions League.
Solet - who stands at 6ft 3in tall - boasts two goals and four assists from 80 games in a Salzburg jersey, and his contract with the Austrian champions runs for another two years.
However, the Daily Mail claims that both Newcastle and Everton are hoping to bring Solet to the Premier League, but they are not the only English teams vying for his signature.
In the same report, Solet confirmed that a move to the Premier League interests him, stating that the prospect of competing in the top tier of English football "excites me a lot".
Inter Milan and Torino are also believed to be keeping tabs on the former France Under-20 international, who is yet to make his first appearance for the Bleus senior team.
Finally, Rennes have reportedly identified two former Premier League players as possible replacements for Chelsea-bound teenager Lesley Ugochukwu.
The 19-year-old is believed to be on the verge of completing a £23.2m switch to Mauricio Pochettino's side, and Rennes will dip into the midfield market should his transfer go through as expected.
According to L'Equipe, former Chelsea midfielder Tiemoue Bakayoko is one of two names under consideration following his exit from Stamford Bridge as a free agent earlier this summer.
Bakayoko failed to live up to expectations during his underwhelming period in West London and has spent the last two years on loan at AC Milan, but he played just three times for the Rossoneri last season.
In addition, ex-Manchester United man and current Roma lynchpin Nemanja Matic is also of interest to Rennes chiefs, as the 34-year-old may struggle for game time under Jose Mourinho next year if Renato Sanches arrives alongside new signing Houssem Aouar.
Matic will turn 35 on Tuesday and is only under contract for another year, but he chipped in with two goals and three assists in 50 matches last season as Roma finished as runners-up in the Europa League.