The former Rangers striker, who has scored just once since signing for the Teesside club in the summer, was dropped by Strachan after a 3-0 defeat at QPR, and his lack of action has reportedly prompted Scotland boss Craig Levein to tell Boyd he will not be in the squad when it is publicly announced on Thursday.
When asked if he would be surprised if Boyd was absent from the pool, Strachan responded: "No, because I know the squad. We always get a squad, it's given to us."
The former Celtic boss, who is likely to see defender Stephen McManus and midfielder Barry Robson called up, is not sure whether Boyd's absence would be a good thing for his club.
"Sometimes you can send players away on international duty and they are a bit down, they go there, score a couple of goals, have a good time and come back," Strachan said.
"Sometimes you can send them along feeling great about themselves and they have an horrific international thing and have a big axe on their head in the Daily Record or the Scottish Sun in the morning.
"You have not been an international player in Scotland until you have had a big axe on your head. If Kenny Dalglish and Graeme Souness can have axes on their heads, then any of us can."
Boyd, who has scored seven goals in 17 internationals, is unlikely to be feeling great about himself following a difficult start to his career in England but Strachan was full of praise for his attitude.
The 27-year-old has faced accusations throughout his career that he does not work hard enough, but Strachan has no such concerns about his approach to training.
"I can't ask for any more from his training. As a matter of fact, I told him last week not to do any more than he has been doing. I have not got a problem with him at all," said Strachan.
Source: PA
Source: PA