But the former Brentford keeper does face fierce competition for the spot from academy graduate Alex Palmer.
The Baggies are open to selling to Johnstone this summer, with the England international having just one year left of his contract at The Hawthorns.
West Ham saw a derisory offer in the region of £6million rejected earlier this month, while Arsenal are also keen on the 28-year-old – with Albion believed to want around £12million for their current player of the year.
Should an acceptable bid fail to arrive before the season gets under way, it is likely Johnstone will start the season in Albion’s goal.
But if he does depart, Button’s Championship experience is currently giving him the edge over Palmer in the race to be the Baggies’ new number one.
The shot-stopper has spent the last three seasons being a Premier League understudy, but prior to that made 152 Championship appearances during spells with Brentford and Fulham.
If Button does start the season in goal, Palmer is likely to get an opportunity to put him under pressure by starting in Albion’s cup games.
Despite being yet to make his Albion debut, the 24-year-old is highly thought of at The Hawthorns.
And after impressing in League Two with Plymouth before shining in League One at Lincoln last season, the club feel he is ready to battle for a starting spot in the Championship.
Teenager Josh Griffiths is another goalkeeper who is aiming to be Albion’s number one long-term.
The England under 21 international impressed on loan at Cheltenham last season.
But with fans not in stadiums last year due to coronavirus restrictions, it is understood the Baggies favour sending the Hereford-born youngster out on loan again next season.
Lincoln, Portsmouth and Cheltenham have previously been linked with a move for the 19-year-old.