Griffiths, who enjoyed a successful loan at Lincoln last season, has been heavily linked with a temporary switch to Portsmouth.
But Albion’s number one jersey is currently up for grabs following the departure of Sam Johnstone.
David Button is currently in pole position, with Alex Palmer expected to be his understudy.
Griffiths, though, has long been tipped as a future Albion number one by those inside The Hawthorns.
And after Palmer picked up a minor injury, the 20-year-old made his first appearance for the Baggies first team during the pre-season friendly against Leyton Orient on Monday.
“Alex Palmer had a slight hip flexor problem, but I’ve wanted to see the young one (Griffiths),” Bruce said. “He’s going to be some goalkeeper, the young lad, I have to tell you.
“I’m really, really pleased. His kicking, everything about him. He’s got a wonderful stature.
“He’s done very, very well.”
Meanwhile, defender Dara O’Shea believes Albion’s recent trip to Portugal was the ideal start for their pre-season preparations.
The Baggies spent 10 days at a warm-weather training camp in Portimao before beating Leyton Orient in a friendly.
“Pre-season’s been great so far,” O’Shea said. “It’s been tough, we’ve had to work hard and dig in and see where we are mentally as well as physically.
“But the gaffer’s been good with us. We’ve all enjoyed it and it’s been a good buzz, it’s been good for the guys to get around each other as well for the team morale.
“Obviously, there’s lots of young lads stepping up too so it’s a good time for them to integrate into the team and that’s what we need.
“But it’s been good , everyone’s fit, everyone’s healthy.
“And it was good to get a game against Leyton Orient and get some minutes in the legs.
“Nobody wants to do all the running so to play games is nice – it was good to finish off a nice training camp with a win.
“It gives us a bit of confidence. To start off on a good note is great, so we’re all happy.”