Rangers have not yet made an improved offer for Kyle Lafferty after Hearts rejected their initial bid last week.
It had been reported that the Ibrox club would return with a fresh approach after the Tynecastle club rejected an initial £200,000 offer.
Hearts considered the bid well short of their valuation for a player who scored 19 times in 44 games last season.
The Northern Ireland international, 30, spent four years at Ibrox before leaving in 2008.
He subsequently had spells at Sion, Palermo, Norwich, Turkish club Caykur Rizespor and Birmingham City.