The former Crystal Palace right-back has been in excellent form at St Mary's over recent seasons, eventually establishing himself as England's first-choice right-back after making his senior international debut in the Euro 2016 qualifying victory over Slovenia in November 2014.
As well as helping to attract attention from Old Trafford and Stamford Bridge, the consistency of his performances at club level have contributed to Southampton enjoying an impressive maiden campaign under the management of Ronald Koeman.
The Saints were widely tipped to struggle in 2014-15 after losing manager Mauricio Pochettino and a host of valuable first-team players in the summer of 2014, yet have comfortably belied such gloomy pre-season expectations to occupy a place in the Premier League's top six.
A minor blip in February, when Koeman's side secured only one victory in five top-flight games, effectively ended any lingering hopes of qualification for the Champions League yet a place in the less reputable Europa League is certainly still achievable with six fixtures remaining.
And while Clyne insists he is focused on helping Southampton finish as strongly as possible, he admits he is eager to experience life in Europe's elite club competition and compete for domestic silverware.
"It's always good to have teams looking out for you, it shows how well you've been doing all season. I am going to take that, and keep on performing and be the best player I can be," he told Sky Sports.
"Right now I'm concentrating on playing for Southampton, there are still games to play, and try to push for that fourth spot. I am an ambitious person and I want to play Champions League football. To win the title and the FA Cup, that is what I want."
Despite Antonio Valencia covering the position with confidence under manager Louis van Gaal, Manchester United could well have an opening at right-back next season with Rafael expected to leave the club having started just seven games in all competitions since the Dutchman's arrival.
Chelsea's need is less obvious, though, with versatile duo Branislav Ivanovic and Cesar Azpilicueta both capable of fulfilling that role to a high standard.
Clyne is out of contract in 2016 and is believed to have delayed talks over a possible extension to his stay on the south coast until the end of the season.