The Icelandic midfielder has become a cult hero for the Dons in his short time at Pittodrie, with banners made in his honour.
And the fans' love affair with 'Arnie' has been cemented by him scoring superb goals at Tannadice and Ibrox in 2012.
Arnason's agent is former Aberdeen player David Winnie, and his agency's brochure states that Arnason has a minimum salary requirement of £5000 gross per week, and it appears that Aberdeen would have to smash its already-hefty (in SPL terms) wage structure to match that number.
An Aberdeen FC spokesman said: "We made Kari an exceptionally good offer, however the player believes he can earn a better deal elsewhere and it looks like he'll be moving on at the end of the season.
"Reports that the club is willing to sell the Icelandic international in the current transfer window are wide of the mark though as he is crucial to our plans for the remainder of the current campaign, both in terms of climbing up the SPL table and enjoying a fruitful run in the Scottish Cup."
29-year-old Arnason, who has played 17 times for his country, has made 24 appearances for the Dons this season following his move from Plymouth last summer.