Utrecht are seeking a fee of around €10m for Kerk, 24, but the maximum bid so far has been €7m from Cagliari.
However, Leeds are close to agreeing a sum that is close to what the Dutch club want.
Kerk has three years left on his contract, but has indicated he is open to a foreign adventure.
In last season’s Eredivisie, Kerk scored 10 goals and contributed eight assists in his 24 appearances.
Kerk is a product of Utrecht’s youth system and has been with the club since 2012.