The Express & Star says out of contract in June, Johnstone's performances for both club and country have led to a host of top-flight clubs sending scouts to watch him in recent months.
Now established in the England set-up, Johnstone knows he needs to be playing Premier League football at the start of the 2021/22 season to have a realistic chance of going to the World Cup.
The 28-year-old has held talks with Albion about extending his contract at The Hawthorns.
But Premier League clubs are circling with the keeper potentially available on a free transfer this summer.
In a bid to jump ahead of the queue, Southampton are believed to weighing up a bid for Johnstone this January.