The 30-year-old quit Ibrox four years ago but is now poised to sign on once again and link up with former forward partner Kenny Miller.
Boyd has also received an offer from Kilmarnock, who he scored 22 goals for last term, and French side Nimes, but Ibrox is his preferred destination.
And it is Gers gaffer Ally McCoist who looks set to win the race to secure the prolific marksman as the former fans' favourite edges closer to a deal that will see him spearhead the Light Blues' bid for the Championship title.
Aberdeen boss Derek McInnes said: "I think if Rangers make Kris Boyd an offer then financially it would beat our offer.
"If it isn't Kris Boyd, then we move on. If Kris decides he wants to come to Aberdeen, then we will do a deal, but we can't stand about waiting for that to happen."