With the Saints' relegation, it was always almost certain that their better players would leave for pastures new, with most presumably hoping to stay in the Premier League.
Kyle Walker-Peters was arguably Southampton's best performer last season in what was a very difficult campaign for the South Coast club, one that seemingly inevitably ended with the drop back to the Championship as they finished bottom.
The 28-year-old Englishman is a strong all-round defender and he is versatile too, able to operate at both right and left-back as well as in midfield.
Everton have, since the end of the season, seen a large number of players out of contract, and many depart the club, leaving lots of gaps in what was already a small first-team squad.
One area of the team where there is, in theory, enough depth, is right-back. The Toffees currently have Seamus Coleman (one player who has signed a new deal) and Nathan Patterson available in that position.
But Coleman is 36 and surely will spend more time next season either as a reserve or possibly even beginning a coaching career, and Patterson has had terrible bad luck with a series of injuries and does not appear to have manager David Moyes' confidence either.
Additionally, the club only have one senior left-back in Vitalli Mykolenko. The Ukrainian international is generally a reliable and decent defender and can be effective when he gets forward, but there is certainly a need for competition, giving Moyes an alternative.
After apparently pursuing Manchester City's Kyle Walker, bringing in his very close namesake could solve both these issues, giving Everton a player who can operate on either flank and offering the Blues a solid and reliable performer.
Everton tried to get another right-back who was out of contract with their earlier pursuit of Fulham's Kenny Tete. But the Netherlands international eventually decided to stay in West London.
While there may be other full-backs out there, Walker-Peters is experienced in the Premier League and available for nothing now, meaning the Toffees can save their transfer pot for other targets, but Everton need to move fast to ward off other suitors and avoid another disappointment.
Getting this one done quickly would also allow the club to concentrate on other targets, especially for the attacking positions the Blues urgently still need to fill.