Both centre-backs have impressed at the World Cup this year, with Colombia's Mina scoring a record-equalling three times from defence, while Vida has been an integral part of Croatia's push to Sunday's final.
Everton can expect their respective fees to rise on the back of those performances but that supposedly doesn't deter them.
Moves for both would secure a brand new, and potentially game-changing, defensive partnership for the club and being willing to spend big on that signals something of a new approach for Everton.
Last summer saw the club spend a record amount of money all over, trying to revolutionise the entire team in one go. This is different, however, and while other signings will surely arrive, the defence is clearly a targeted area.
As it should be - Ashley Williams and Phil Jagielka are both far past their best and need replacing if Everton have serious ambition.
Replacing both at once is certainly ruthless but it's with Michael Keane that Everton appear truly cutthroat.
Keane arrived for big money last summer but was unable to look like the long-term answer for Everton at centre-back. If the club really are set to replace him just one year later, it suggests that this really is a new Everton - one that will not waste time if they're unsure.
It's ruthless - but it might be exactly what Everton need right now.