Josh Brownhill, who just enjoyed a stand-out season in the Championship with Burnley while scoring eighteen goals, is out of contract at the end of June and has so far failed to agree on an extension with the newly promoted side.
That has alerted several Premier League clubs, with West Ham United also said to be interested in the 29-year-old Englishman.
Everton have plenty of their own players out of contract at the end of this month, so they are familiar with this situation.
Several, including, Abdoulaye Doucoure, have already announced they are leaving the club, and Idrissa Gueye, Dominic Calvert-Lewin, and Michael Keane are still to sign new deals.
Manager David Moyes, therefore, has a big rebuilding task during the summer and needs major reinforcements throughout the first-team squad.
One area of the team that Moyes is apparently focused on is shoring up the midfield. Although Carlos Alcaraz has signed a permanent deal and Gueye is very likely to, the midfield might still lack sufficient numbers and strength in depth, especially with Doucoure's departure.
Apart from these players, Everton only have James Garner, Tim Iroegbunam, and a player, Harrison Armstrong, who is still, in Premier League terms, an inexperienced youngster, available in the engine room.
Brownhill is an experienced player, and Moyes is known to be an admirer of his and reportedly tried to sign the midfielder when he was at West Ham.
He is a very versatile individual who can operate in a number of positions in the middle of the park, while he has spent the majority of his playing time recently at Burnley in a deep-lying defensive midfield role.
The Championship is a potentially fruitful hunting ground for the Everton manager as he seeks affordable and good-quality talent for next season.
So, although he is almost thirty and the club need to focus on younger players, bringing in Brownhill on a free transfer could make a lot of sense for the Toffees boss. Given his experience and attributes, it would likely be a no-lose scenario for the Blues if they could get him for free.