McInnes had been hopeful of luring the Kilmarnock favourite to Pittiodrie this summer, and has already held talks with the 30-year-old.
But the Dons boss fears Boyd may opt to drop down to the Championship to play for Rangers, should the Ibrox club come in with an offer.
Boyd scored 22 goals for Killie last season, and McInnes expects to hear an answer from the player’s representatives in the next 24 hours.
“I was aware of Rangers' interest last week, and if Rangers make Kris Boyd an offer, I think financially it would beat our offer,” McInnes told Sky Sports News.
“But I’ll have an update probably today or tomorrow on that, and if it’s not Kris Boyd we move on.
“We did declare an interest in him. We spoke to him and if Kris Boyd says he wants to come to Aberdeen we’ll do our best to do a deal.
“But we can’t be standing about waiting for that to happen. We’ve still got other options to look at as well."