That's according to local outlet the Express & Star, who suggest that the Whites are eager to snap up the 28-year-old if and when the Baggies are relegated from the top flight.
For his part, it is understood that Johnstone is determined to walk away from the Hawthorns at the end of the season if Albion suffer an immediate relegation back to the top flight.
That’s understandable for a stopper in his prime who has only just played his way into the England squad.
And Leeds are said to be one of numerous clubs who are keeping tabs on him.
The Athletic suggest that Tottenham are also in the running, and lead the race at this early stage.
But a new goalkeeper could become an increasing priority for Leeds as the summer progresses, especially if they manage to offload veteran Spaniard Kiko Casilla, as Football Insider claim they are looking to do.
That would leave Illan Meslier as the only proven senior goalkeeper at Elland Road, and an understudy – or competition – would be a necessity.
Johnstone has been rare bright spark for the Baggies in a dour season, and has garnered praise from the likes of Gary Lineker, despite conceding 57 goals in 29 matches in the Premier League this term.
Elsewhere, Leeds are said to have made a decision on their reported interest in PSV Eindhoven starlet Noni Madueke.
The young forward, who is capped at U21 level for England, has hit seven goals and six assists in 20 league outings this term, and Football Insider suggest that the Whites have made contact with his current club over a potential summer swoop.
But their advances were met with suggestions that Madueke will cost around £20-25 million in the coming months – a price that Leeds are reportedly unwilling to meet.
It is claimed that Marcelo Bielsa's men are expected to be active in the transfer window, but don't have a “bottomless pit of cash” to draw upon.
We’ve gathered the rest of today's Premier League speculation below...