Rangers want to sign another striker this summer and are pushing to sign the 28-year-old forward from PAOK in the ongoing transfer window.
The Gers failed with a bid to sign him last week but have been more than prepared to continue to press forward with an attempt to sign Colak, with a fresh proposal going in.
However, according to Greek daily Sportime, PAOK have knocked back the bid from Rangers for the forward.
Rangers put in an improved offer but it was still not good enough to convince PAOK to clear his sale this summer.
The new bid is claimed to have been around €2.3m and it was short of what the Greek side want for Colak.
It has been suggested that a bid of around €3m would convince PAOK to sell the striker ahead of the new season.
Colak is keen on joining last season’s Europa League finalists, but is being made to wait as the two clubs continue to haggle over the transfer fee.