Iceland's Gylfi Sigurdsson attends a news conference
The Icelandic international would could cost up to £25 million if he moves to Merseyside - providing he accepts the move.
Four years ago he had the chance to move to Liverpool, and snubbed the offer from the Reds to join Tottenham instead.
“Look at where Spurs have finished in the last few years, compared to Liverpool, and look at the squad here. It’s a fantastic team and with the new training ground, possibility of a new stadium, it’s exciting times.”
While that statement may well still ring true in 2016, Sigurdsson has not been a part of it.
Swansea's Gylfi Sigurdsson
He was sold in 2014 after failing to establish himself as a regular, with Christian Eriksen's arrival making it tricky for him.
Yet he maintained he had no regrets, telling The Mail: "With the Brendan [Rodgers, who managed him at Swansea] link in the Press it seemed it was more likely I'd go there but Tottenham showed a lot of interest in me and at that time they had players like Gareth Bale and things looked really good.
"Obviously there have been plenty of changes over the past two years and new faces have been brought in but I will always remember my time as a positive one."
Iceland's Gylfi Sigurdsson shoots at goal
Sigurdsson has re-established himself at Swansea City, and starred at Euro 2016 with Iceland.
Now he appears to have the chance to really make Liverpool not pushing harder to convince him to sign four years ago - by signing with their rivals Everton.
New boss Ronald Koeman is working hard to recruit players since being appointed, and Sigurdsson is a proven Premier League performer who is approaching his peak years.
He could be an excellent signing for the Toffees, even if he is an expensive one.
Gylfi Sigurdsson celebrates scoring the second goal for Swansea with Leroy Fer