The Daily Star says the Championship outfit have rejected an initial bid of £12m from the Clarets and are demanding in the region of £20m.
But the Clarets are not prepared to go above £15m and will make an improved take-it-or-leave-it offer in the next 24 hours.
Clarets boss Sean Dyche is desperate to land the New Zealand hitman - but will look elsewhere if Leeds continue to drive the price up.
A source said, "Chris knows his stock has never been higher and wants a crack in the Premier League.
"But he also knows Leeds have to be realistic in their valuation and not hold out for a fee that is over the top."