Aberdeen have decided to cash in on Miller as his contract expires in the summer and he had yet to agree a new deal.
Strachan watched Miller in action in midweek and Aberdeen manager Mark McGhee has confirmed the two clubs were talking again today.
McGhee: “Middlesbrough have asked about Lee Miller. They have made an approach and the clubs are talking.
“I do not want to lose him because he is a top player but I have to be mindful of the fact that Lee is out of contract in the summer.”