Aberdeen are waiting to hear whether their midfielder Kari Arnason will remain at Aberdeen when his contract runs out at the end of the season.
The Iceland star scored the Dons' opener in their 1-1 draw at Ibrox and team manager Craig Brown is keen to secure his services on a longer term.
"He has been made a very good offer from Aberdeen and hopefully he will give his decision soon," said Brown.
"I think he will be in demand because you can see his ability."
Arnason moved to Scotland's north-east last summer after leaving Plymouth Argyle and previously played for Vikingur, Djurgarden and Aarhus.
His 63rd-minute strike at Ibrox put Aberdeen on course for their first win at Ibrox since 1991 but they were pegged back by Rangers midfielder Maurice Edu only four minutes later.
On Arnason's choice of club after the summer, Brown told BBC Scotland: "His agent, David Winnie, is a former Aberdeen player. Hopefully that will weigh in our favour.
"He scored a wonderful goal at Tannadice recently and scored an excellent goal here [at Ibrox].
"Arnason is a fine player and we hope to keep him but at the end of the day it will be money that will count."
Aberdeen had brought Rory Fallon and Josh Magennis into the side in place of Andrew Considine and Mohamed Chalali, while Rory McArdle passed a late fitness test to start.
And given the Dons' injury concerns, Brown was delighted at his players' performance.
He said: "I'm proud of a makeshift team today. They did exceptionally well considering five first-team players weren't available.
"Four of the starting team were eligible for the Under-21 list.
"We've got to supply three Under-21 players in the squad for ever SPL game.
"It's a very good idea of Stewart Regan's to make it an incentive: rather than fine clubs, he is giving awards for producing young players, so we get £1,000 for three or more. It's a bonus for Aberdeen."
Reflecting on a pulsating 90 minutes, he added: "We defended very well. We got a break or two but so did Rangers when Arnason's header hit the top of the bar in the first half.
"I'm really disappointed we didn't win the game, having got in to a winning position, but I suppose a draw was a fair result.
"Our two most important games are the next two - Dunfermline at home next week and Queen of the South in the Cup.
"They are more important than this game at Ibrox. I told the players that.
"Every team outwith the Old Firm will agree, anything you get in an away game against the Old Firm is a bonus.
"But we can't afford not to get points next week and in the Cup game we can't afford a slip-up against Queen of the South.
"There can be no complacency."
Brown revealed fears that Rob Milsom's season could be over following knee surgery.
He said: "He is likely to be out for the season.
"He had a knee operation in London yesterday and the leg was examined and there was more damage than first feared.
"The surgeon said he will not play this season so that's a major blow for us."