Johnson, who is out of contract at the end of the season, has been linked with Chelsea, Manchester City and Wolves in recent months.
The 24-year-old cannot leave for free and a tribunal is expected to set his price.
“I think Adam will stay at the club in this window,” said Strachan.
“I think he’ll still be here when the window shuts, one way or another. He likes playing for the club, he’s a good kid, and he would like to try to get us back to the top level.
“It’s not in our favour that his contract is up, but we can take solace from the fact that Manchester City got a half-decent deal for Sturridge. There’s always that in the background.”
