The 22-year-old has been linked with Sunderland, Fulham, Everton and Birmingham.
Strachan told The Mirror: “Adam Johnson’s record this season is phenomenal. He is one of our best players. His record and the club’s results run hand in hand. He’s a terrific player.
“I am hoping that over time we can gradually get to know each other.
“I don’t think you can have a big conversation just like that. I want to get to know him. All I can say is that since I’ve been here he’s handled himself brilliantly.”
Johnson’s contract with Middlesbrough expires at the end of the season.
“I’ve seen players whose contracts are up affected by their situation,” added Strachan. “But it’s not affected this kid.
“We’ve got some good players. We’ll try to bring on the younger players. That’s what I love about coaching – making players better.”
