Kilmarnock manager Steve Clarke has described Rangers' bid for Jordan Jones as "nowhere near acceptable".
Killie turned down a reported £350,000 offer for the 23-year-old Northern Ireland winger, who is under contract until the summer of 2019.
Clarke said: "There's been a bid, nowhere near acceptable. I would be a little bit sad if I was the player, to be honest, that the bid was so low.
"It was an easy one for the club to turn down."
Rangers look set to have more joy with attempts to sign Jason Cummings and Russell Martin on loan.
Cummings arrived in Glasgow on Sunday night after being left out of the Nottingham Forest squad for Saturday's defeat by Aston Villa, Aitor Karanka's first match since replacing Mark Warburton as boss.
The 22-year-old has scored four goals in 10 starts and seven substitute appearances since leaving Hibernian for Forest in the summer.
Martin looks set to arrive on Tuesday. The 32-year-old has not featured for Norwich since a 4-0 defeat to Millwall on August 26 and subsequently lost his place in the Scotland squad.
Rangers also made an enquiry over Hamilton midfielder Greg Docherty last week after completing earlier loan deals for Sean Goss and Jamie Murphy.