Liverpool manager Jürgen Klopp
Jürgen Klopp is expected to be extremely busy during this summer's transfer window, as he looks to build a squad that is capable of making a sustained challenge for major trophies, both domestically and on the continent.
Over at Goodison Park meanwhile, Ronald Koeman has extravagant plans of his own, having already spent in excess of £47 million on adding new talent to the Toffees squad.
Klopp should step in though, and strike a severe blow to the Blues' hopes of usurping Liverpool next term, by poaching the Iceland international from their grasp.
The 27-year-old was in sensational form for the Welsh outfit last term, scoring nine goals and registering 13 assists in 38 Premier League outings.
The talented play-maker would be a superb addition to the Reds' squad, and would provide excellent competition for Giorginio Wijnaldum in the heart of Liverpool's engine room.
The Reds boss will be well aware of Sigurdsson's talent, after the Swansea man ran the show during his side's shock 3-2 win over Liverpool at Anfield last season.
Swansea City's Gylfi Sigurdsson
He would offer Klopp's men something that little bit different, and would provide them with a totally different dimension to their build-up play, what with his expert vision and the fact that he is a set-piece specialist.
Whilst £40 million seems like a lot of money, the Icelandic star is well worth that, with the kind of contribution he makes week-in, week-out, and beating Everton to his signature would make the signing of the Swans midfield all the more significant for Liverpool.
Swansea City's Gylfi Sigurdsson in action