Rangers say they have rejected a £9m offer from an unnamed club for striker Nikica Jelavic after warding off an earlier approach from Leicester City.
The Championship club had a £6.5m bid turned down by the Scottish champions.
Leicester then had a bid of more than £4m accepted by Everton for forward Jermaine Beckford
But a Rangers source claims that they have since received a call from an agent offering substantially more but refused to name the interested club.
Leicester were seeking a new striker after missing out on signing Shane Long, who joined West Brom from Reading.
“I'm sure he will be a world-class player by the end of his career”
Rangers sources had stressed that they would be unwilling to allow Jelavic to leave unless someone offered "silly money" for the Croatia striker.
And fellow Ibrox striker Steven Naismith was eager for the player to remain in Glasgow.
"He has been a massive player for us since he has been at the club and hopefully we can keep him," said the Scotland international ahead of the closure of the transfer window.
"He is a top-class forward and in football years he still has a bit to go before he reaches his peak.
"I'm sure he will be a world-class player by the end of his career."
The 26-year-old Jelavic joined Rangers for £4m from Rapid Vienna in 2010.
- Former clubs: Hajduk Split, Zulte Waregem, Rapid Vienna
- Capped 12 times for Croatia, two international goals
- Won Scottish Premier League and Scottish League Cup in first season at Rangers
Despite an ankle injury early in his Ibrox career, he finished his first season in Glasgow with 19 goals.
Jelavic has scored three goals in seven appearances this season but was among the culprits who missed goalscoring chances as Rangers were knocked out by Maribor in last week's Europa League play-off.
Big-spending Leicester were desperate to improve their strike force having failed to sign Long and having had bids rejected by Bristol City for Nicky Maynard.
This week, they cancelled Slovenian striker Leon Crncic's contract by mutual consent, they have also told fellow forward Martyn Waghorn he has no future with the Foxes, while Dany N'Guessan has headed for Millwall.
They turned their attention to Jelavic, who began his senior career with Hajduk Split before spells with Zulte Waregem and Rapid Vienna and has been capped 12 times for his country.
However, despite heavy debts, Rangers held on to Jelavic on a quiet transfer deadline day for the Scottish champions.
Out-of-favour striker James Beattie had his contract terminated, while Andrew Little, Kyle Hutton and John Fleck were sent out on loan to English clubs.
Meanwhile, reports in Africa claimed the Ibrox club had a £100,000 offer for South Africa midfielder Siphiwe Tshabalala rejected by Kaizer Chiefs.