Johnstone has been in outstanding form the Baggies this season with the 28-year-old having made more saves than any other keeper in the top flight.
That form saw him called up to the senior England squad for the first time back in March.
But it has also led to admiring glances from elsewhere – with Johnstone having just one year left on his contract at The Hawthorns.
West Ham are understood to be keen, with the Hammers believed to want a new number one to replace Lukasz Fabianski, who turned 36 on Sunday.
Manchester United – the club where Johnstone began his career – will also need another goalkeeper this summer if they sell David de Gea.
While Tottenham and Leeds have previously been linked with a move for the Preston-born shot-stopper.
Allardyce is still battling to keep Albion in the Premier League – with top-flight football something that is sure to be important to Johnstone moving forward.
And the boss said any decision on Johnstone’s future won’t be made until Albion know what division they are in next season.
“We can only discuss that when we have secured our position as a Premier League club,” the boss said when asked about Johnstone’s future.
“That would mean discussion from the hierarchy at the club and look at what they can do with Sam’s contract and try to persuade him to stay.
“As usual, business is business. Whatever happens can only be decided then, but I think the club would do their very best to keep him.”
Elsewhere, Albion’s under-18s could face Villa in the semi-finals of the FA Youth Cup – but they have to overcome Everton first.
The young Baggies thumped Tottenham 5-0 last week to reach the quarter-finals.
They will now face Everton at The Hawthorns on April 27.
The winners of that will then face either Villa or Newcastle for a place in the final.