Rangers chairman Douglas Park has told the club's AGM that Alfredo Morelos and Ryan Kent's Rangers contract demands may be "unattainable".
Both players are out of contract at the end of the season and able to speak to other clubs from January as they enter the final six months of their deals.
Winger Kent has failed to show his top form his season, while Morelos is now second-choice striker behind Antonio Colak.
Colombia international Morelos was dropped by former boss Giovanni van Bronckhorst ahead of their Champions League play-off second leg against PSV Eindhoven after concerns about his attitude and fitness.
The Ibrox supporters asked for answers about both players at the club's AGM in Glasgow on Tuesday morning.
One shareholder asked why neither had been sold last summer with the club facing the prospect of losing players who had been, in previous seasons, two of their most valuable assets.
Sporting director Ross Wilson initially took the question: "They've not been allowed. Two parties need to commit.
"Ryan and Alfredo are in different situations but there is a willingness for the boys to stay with us from the club."
He also revealed a bid for both had been knocked back due to not meeting the club's valuation.
Wilson added: "Why didn't they go in the summer? We've rejected one offer for both players on the basis the players were of more value and we went on to be league champions in that same season."
Chairman Douglas Park then suggested that Rangers had made the best offers they could.
"The board tried to negotiate and sometimes if the terms are unattainable you have to accept you have done your best."
Morelos and Kent are among 11 Rangers players out of contract at the end of the season.
In an exclusive interview with Sky Sports News, new manager Michael Beale said he was hopeful his relationship with the players will would help with negotiations, insisting it was not just for them to decide.
"They are two players I've worked well with previously," he said.
"When I was here previously they were both excellent in different ways.
"In Alfredo, in terms of the goals he scored, and Ryan in terms of the way he entertained people and got on the ball and took the game to the opponent.
"I think they're capable of more than they're showing right now, that's fair to say, but they'll have their own reasons for that and they'll be working away at that.
"I trust both players and we've played this out as a club before with Connor Goldson and his contract situation.
"Sometimes a player wants to see and take their time, there's no problem, it's fine. I think the option is both ways with the players, the cards aren't in Ryan and Alfredo's hands.
"We also want to create a stronger Rangers going forward, with or without those players. Ideally with them."
December 15: Hibernian (h), Scottish Premiership, kick-off 8pm, live on Sky Sports
December 20: Aberdeen (a), Scottish Premiership, kick-off 8pm, live on Sky Sports
December 23: Ross County (a), Scottish Premiership, kick-off 7.30pm, live on Sky Sports
December 28: Motherwell (h), Scottish Premiership, kick-off 7.45pm
January 2: Celtic (h), Scottish Premiership, kick-off 12.30pm, live on Sky Sports
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