Real Madrid's Mateo Kovacic (L) in action against Shakhtar Donetsk's Fred
The Toffees are expected to splash the cash this summer as new manager Ronald Koeman has arrived, with the Dutchman set to spend Farhad Moshiri's millions.
Meanwhile, West Ham boss Slaven Bilic will be given money to spend, and having already made two free transfer signings, the Croatian may well have saved some money to made a huge signing.
Now, the Daily Mail report that both clubs have in fact been offered the chance to land Real Madrid youngster Mateo Kovacic, though their £30m asking price is something of a problem for the two Premier League sides.
Kovacic, 22, emerged as one of the top Croatian talents during his time with Dinamo Zagreb, and his potential earned him a big January 2013 move to Inter Milan.
After eight goals in 97 games, Kovacic was then sold on to Real Madrid last summer, but he started just 11 games for the club as he failed to displace the likes of Casemiro, Toni Kroos and compatriot Luka Modric in the Real Madrid midfield, though he did win the Champions League last month.
Now looking for games, Kovacic - who has been at Euro 2016 with Croatia - has been offered up to Everton or West Ham, but with the £30m asking price so far proving to be an issue, Madrid may be willing to loan the player out instead.
That could be particularly appealing to West Ham boss Bilic, who, as a fellow Croatian, will be very familiar with what Kovacic can do, and could offer even more creativity to an already exciting West Ham midfield.
Would you like to see Everton or West Ham splash the cash on Kovacic?