The Toffees have spent heavily over the preseason period - making Merlin Rohl and Tyrique George's loan moves into permanent deals - alongside landing Hayden Hackney, Christian Norgaard and Brennan Johnson.
David Moyes is also rumoured to be tracking long-term target Liam Delap at Chelsea, but Football Insider claim the veteran Scottish boss is also keen on Bournemouth's Marcus Tavernier.
Moyes is looking to add more firepower to his attack on Merseyside and Tavernier is a favourite of the former Manchester United manager according to his old scout Mike Brown.
"Tavernier is a good player, and he would fit in well at Everton.
"He's exactly the type of player Moyesey loves, works hard, plays in multiple positions, always makes himself available and he's good with the ball at his feet."
Everton have flagged their interest to Bournemouth, but no formal bid has been made at this stage, as the Cherries are not actively looking to sell.
Tavernier impressed as Bournemouth secured a first-ever European qualification under Andoni Iraola last season - with seven Premier League goals scored - and he could be available for around £25M if Bournemouth allow an exit.