Boyd, 30, scored 22 goals for Kilmarnock last season but is now a free agent.
McInnes has pitched the Pittodrie club to the Scotland internationalist, who has also been linked with Dundee United and French side Nimes, and the striker is now considering the offer to join the League Cup winners.
Aberdeen begin their Europa League qualifying campaign on July 3. "I managed to meet and talk with Kris and also talked to his agent," McInnes admitted.
"We have had a discussion and said we would like to bring another forward into the club.
"We have made a pitch of what Aberdeen can be as a club for Kris. Kris has a few other options and wants some time to consider them."