West Ham have offered £7m for Rangers striker Nikica Jelavic, BBC Scotland has learned.
The English Championship leaders have been in negotiations with the Ibrox club for more than a week.
Rangers though, believe the 26-year-old is worth more and could hold out in the hope of an improved bid from elsewhere before the transfer closes next week.
Manager Ally McCoist wants any deal concluded quickly so that he has time to find a replacement.
McCoist has already described a reported £6m bid from the Hammers for the Croatian international as "not nearly enough" and says no formal bid has been received.
However, BBC Scotland understands that West Ham have come forward with an offer for Jelavic. Liverpool and Fulham have also shown interest in the player.
Jelavic, who has scored 30 goals for Rangers, made the switch to Glasgow from Rapid Vienna in 2010 and helped deliver the title under Walter Smith last season.
Rangers have already concluded business this month with the arrival of Swedish midfielder Mervan Celik from Gais of Gothenburg.
They ended their interest in St Johnstone striker Francisco Sandaza after he turned down the chance to sign a pre-contract agreement.