On the day that midfielder Isaiah Osbourne arrived on a two month loan from Aston Villa, Strachan has outlined his determination to keep Johnson.
The winger is Middlesbrough's leading scorer in the Championship this season, but is being tracked by Sunderland, Everton and Wigan and the lure of Premier League football will be an attractive proposition for the player.
Johnson has been made several new contract offers to extend his stay on Teesside, but the Easington-born England Under-21 international is yet to commit with his current deal expiring at the end of the season.
Middlesbrough will be in a difficult situation in January if Johnson has still not agreed new terms, with Strachan keen to see talks progress.
How can I tempt him to stay I'm sure Steve (Gibson) and Keith (Lamb), who have known him for a long time, have done their best, said Strachan.
I don't think I can do any better. I'm only doing my job and it's very hard for me to sit down with anyone and have a heart to heart with them. I don't know them that well.
When you sit down it's vital that you know them and they know you.
You can then have a conversation and have knowledge of the person, I know Adam the footballer, but not as a person.
We will have to wait and see what happens in January, see where we are, see how we are playing. Circumstances can change in a couple of months, we are not making any promises to anyone.
I believe Steve and Keith have made numerous attempts to sign Adam up to a new contract with Middlesbrough.
I know he is a top player.
For 18 months the club have been trying to get him to sign a new contract. We have to keep working because he is a talented lad, that's for sure.
The Boro boss completed the loan signing of Osbourne from Aston Villa yesterday, six days after adding Marcus Bent on a similar two-month deal from Birmingham City.
I've known about Isaiah for about a year and he'll bring us more strength in the midfield area where we're definitely short on numbers,
said Strachan. He's not a flair player, he's what I'd call a continuity player, but he'll also give us strength, height and get about the pitch.
Osbourne was one of nine names included on a sheet of paper Strachan was holding on the day he was paraded at a press conference at the Riverside Stadium.
The 21-year-old has revealed that Martin O'Neill, who Strachan succeeded at Celtic Park, played a part in his move to the North-East.
Middlesbrough feels like a Premier League club, while I'm looking forward to working with Gordon Strachan,
said Osbourne. Before coming here, I first spoke to Martin O'Neill and Stilyan Petrov about the gaffer and they spoke highly of him.
I'm here for two months and right now I'm looking no further than that, hopefully I will play a few games and can help the team. I played for Nottingham Forest in the Championship last season, so I know a little bit about what it's about.
Osbourne is likely to be involved at Selhurst Park tomorrow.
The Middlesbrough manager has been looking to bring in new faces and he remains on the look out for a new rightmidfielder, having successfully recruited a central player.
Strachan has learnt in the last 48 hours that Emanuel Pogatetz does not need to have a plate inserted into his fractured cheekbone.