Everton have been extensively linked with a move for Maxime Esteve, a French defender who has just enjoyed a standout season for the Clarets as they secured an immediate return to the English top flight.
The Blues face a major rebuilding task throughout the first-team squad as a number of experienced players leave and need replacing.
This, anyway, comes on top of the fact that Everton has one of the smallest squads in the Premier League and needed reinforcements, even before this off-season's numerous departures.
One area of the team affected is, of course, the Toffees' defence, with uncertainty surrounding Michael Keane's future as his contract expires and rumours about Jarrad Branthwaite potentially seeking a move away.
If both these players do leave, Blues boss David Moyes will need to move quickly to replace them and shore up his defence.
That defence was one of the Premier League's most miserly again last season with Everton only conceding forty-four goals, which was only bettered by Liverpool, Arsenal, and Chelsea, all of whom qualified for the Champions League.
Clearly, Moyes needs to retain that defensive efficiency and add a significantly improved attacking threat to push the Toffees up the table.
Esteve is a player who could certainly fit into the team's defence and would be a strong potential replacement for an error-prone and aging Keane, if not necessarily Branthwaite, who has excelled since breaking into the Everton side.
Burnley's 23-year-old is a player who is young and with the potential to get better as time goes on. Esteve is a centre-back who I thought would be a good possible bet for Everton last year, and the last twelve months have only enhanced his reputation.
While Moyes may hold a strong interest in perhaps signing the Frenchman, the Turf Moor club have moved to block any possible bidders by putting a £50 million price tag on him.
The Clarets also have achieved promotion too and so might hope that this will persuade their best players to stay put, at least for another year.