Rangers have already rejected a £7million package from West Ham for Jelavic, who missed Saturday's 4-0 win over Hibernian at Ibrox with a virus.
However, Everton boss David Moyes is eager to boost his attacking options ahead of Tuesday's transfer deadline and Rangers are bracing themselves for an official offer from the Merseysiders.
Everton have funds after selling Diniyar Bilyaletdinov to Spartak Moscow for an undisclosed fee, reported as £5million, but it is understood that Ibrox owner Craig Whyte is determined not to let Jelavic leave for anything less than his valuation of the player, thought to be £8million-plus, and will be more than happy to still have the player at the club on Wednesday morning.
The Ibrox club are also confident that manager Ally McCoist will have at least one new player in his squad before the transfer window closes.
McCoist had expressed interest in signing Pawel Brozek from Turkish club Trabzonspor but the Polish striker has agreed terms with Old Firm rivals Celtic and will join on loan until the end of the season subject to a medical.
