Mark McGhee has already admitted he would consider cashing in on anyone who is a free agent at the end of the season and Boro are believes to have tabled a bid of £500,000.
McGhee told BBC Scotland: Middlesbrough have asked about Lee Miller. They have made an approach and the clubs are talking.
"If a deal is done, it will have to be done very quickly. We have to decide whether we want to keep him or sell."
Strachan, who has also been linked with Celtic's Scott McDonald, attended the Dons' 3-0 win at Hearts on Wednesday night.
That game saw Miller make his return from a three-match SPL ban.