The Serbian midfielder has impressed with his creative displays at St Mary's since completing a £10.9m ($13.9m) switch from FC Twente in July 2014, with Jurgen Klopp now said to be keen on his signature after depriving the Saints of Sadio Mane last summer.
Adam Lallana, Dejan Lovren, Rickie Lambert and Nathaniel Clyne also swapped Hampshire for Merseyside during the reign of Brendan Rodgers.
Earlier this month, Liverpool publicly apologised for any "misunderstanding" regarding Virgil van Dijk and withdrew their interest in the highly-rated Southampton centre-back amid rumours that they had been reported for an alleged illegal approach.
While it is difficult to imagine that the relationship between the two clubs is anything other than strained after that regrettable episode, The Sunday Times understand that Liverpool have now expressed an interest in signing Tadic, also on the radar of West Ham United, as they seek to bolster their ranks ahead of an imminent return to the Champions League.
The same publication claim that the 28-year-old's current contract contains a release clause worth at least £13m and that he would welcome a move having become "disillusioned" with the management of Claude Puel. The unpopular Frenchman is expected to leave his post over the coming weeks despite leading Southampton to an eighth-place finish and the EFL Cup final during his first season after being appointed as the successor to Ronald Koeman.
Addressing his personal situation after helping Serbia to reclaim their place at the summit of Group D in European qualifying for the 2018 World Cup courtesy of a 1-1 draw with Wales in Belgrade, Tadic refused to discuss specific rumours but did not appear to completely rule out the prospect of leaving Southampton.
"I don't comment on these things. I have an agent and I have correct things with the club," he was quoted as saying by the Daily Echo.
He added: "We will see. You never know in football. In every club, sometimes players leave. It is not easy, but this is football."
Tadic, who only put pen to paper on a new four-year contract in August 2016, has appeared 98 times in the Premier League for Southampton, scoring 14 goals and providing 24 assists during a three-year span. His frustration with Puel stemmed from frequently being substituted as part of the manager's much-maligned rotation policy.
Puel claimed in March that the duo had sorted out their issues internally after Tadic, also linked with a potential switch to Serie A, had accused him of a lack of respect.