The Saints lost the likes of Adam Lallana, Calum Chambers and Dejan Lovren last summer, and could now face a similar fate this summer.
The Mirror believe that right back Clyne could be on his way to Premier League rivals Manchester United this summer, which would leave Ronald Koeman with a big hole to fill.
Newcastle's Daryl Janmaat was recently linked with a move to the South Coast by The Mirror, but they now report that Southampton are looking further afield.
They suggest that Evian ace Wass is on their radar, with the Denmark international having an impressive season over in France.
Wass, 25, can play at right back or on the right hand side of midfield, and has hit ten goals in all competitions this season, racking up five assists too.
With just one year left on his contract, The Mirror believe that Wass could be available for just £1.5m as Evian fear losing him for nothing in 2016, whilst they also note that Newcastle United and Stoke City are also interested in signing the former Brondby and Benfica utility man.
If Clyne does leave St. Mary's Stadium, Southampton are likely to be linked with a host of right backs - and now Wass is another name to keep an eye on.