As the Blues step up their search for someone to fill the void left by Gavin Bazunu, it appears the 20-year-old former Cheltenham and Lincoln stopper is the man Danny Cowley will turn to.
But why does the Pompey manager, who targeted Griffiths last season, and others rate him so highly?
Well, the answer to that can be easily found in the glowing references the young stopper has accumulated since emerging through the youth ranks at the Baggies.
Here’s what those who have seen him at close quarters have said about the hugely talented keeper…
Boaz Myhill – West Brom Professional Phase Development Goalkeeping Coach
Speaking after Griffiths’ England under-21 call-up during his loan spell at Cheltenham
‘He’d never get carried away. He’s great from that perspective.
‘There have been some highs and lows, that’s why we sent him to Cheltenham - to learn, with the long-term goal of progressing him through the ranks at our football club.
‘One of his biggest strengths, not just that he’s a good player, is that he’s the kind of boy and man that people will do things for.
‘Everybody likes Josh.
‘It’s all credit to him that he’s having the season that he is.’
Former Cheltenham boss Michael Duff (now at Barnsley)
‘I think his strongest attribute is his mentality.
‘He’s not your stereotypical young lad, so when he gets a bit of recognition he’s not going to roll up next week with a new Rolex and a new car.
‘On the flip side, he’s made a few mistakes along the way and he’s dealt with them really well as well.
‘Goalkeepers have changed. Before, you had to be as mad as a box of frogs and he isn’t that.
‘He’s got a cool temperament, he doesn’t seem to get flustered.
‘As a first year pro, to play in such a pivotal position and to get those sorts of numbers, is a credit to him. If we wasn’t, we wouldn’t pick him.
‘We’d like to think that one day he could go and play in the Premier League for West Brom.’
Steve Book – former goalkeeping coach, Cheltenham
‘The gaffer was worried he looked like a kid, but I said "leave it to me” and the rest is history.
‘He is so calm and if he has a setback he will just say “don’t worry, go again and crack on”.
‘Like Jack (Buckland, who also had a loan spell at Cheltenham), he can be the next big thing and we’ve given them both the platform to kick on.’
Tim Dittmer – former head of goalkeeping at the FA, now head of coaching
Speaking after Griffiths’ call-up to the England under-21s and during Cheltenham’s League Two title-winning season
‘It’s a big ask going straight from academy to men’s football.
‘The dynamic of the dressing room is different and the demands are different. They demand different things of you as a goalkeeper.
‘There isn’t any room to make mistakes because it’s costing the team points, costing managers jobs and costing players money.
‘That gives goalkeepers the opportunity to either thrive in it or go under and Josh has shown a really mature mentality to dominate on aerial balls and make saves.
‘He’s been able to contribute to the team and hopefully he’ll be achieving promotion (with Cheltenham).
‘He’s made mature decisions, he’s recognised when to get involved in the game and when not to and his emotional control has been good.
‘Has he made mistakes during the season? Absolutely. But that is all part of this step on his journey and how he deals with mistakes has been impressive so far.’
Former Lincoln manager Michael Appleton
‘He’s got stronger and stronger (during his time at Sincil Bank)
‘He had a very difficult start as we all know in the first five or six games, but since then his performances have grown and he’s improved with his feet as well.
‘That’s been recognised, not only by myself but by the people at West Brom as well.
‘We knew his capabilities as a goalkeeper – his handling, his shot-stopping skills – but I think we’ve helped him develop as a player, which is part and parcel of the job as well.’
West Brom manager Steve Bruce
Speaking this week after being asked about the current goalkeeping situation at the Hawthorns.
‘We’re very, very happy with what we’ve got (goalkeepers-wise).
‘We’ve got an exceptionally good young goalkeeper (Griffiths) as well who’s been on loan for a couple of years.
‘We’re okay in that department, that’s one I’m not looking at at all.
‘So it’s up to them to fight it out [(or) who’s going to be the number one.’
Joseph Masi – West Brom reporter, Express & Star
‘Griffths is one for the future and is very, very highly thought of.
‘He’s been in a number of England under-21 squads and is only 20.
‘When I started covering West Brom, someone from the club told me he is fantastic, so he is really rated here.
‘He is very much seen as a future Albion number one.’
Jon Palmer – Cheltenham Town reporter, Gloucester Live
‘Having conducted a few interviews with him he’s very mature for his age.
‘Everyone thought “this kid has the potential to play at the top level”.
‘There would have been certain aspects of his game that he needs to keep working on, but in terms of his size, temperament, shot-stopping ability and composure on the ball, I think the only thing he needed to add to that was more and more games.
‘He’s obviously got more experience in League One under his belt after being with Lincoln, although it was cut short by injury.
‘Having seen a lot of good goalkeepers, including Jack Butland and Dillon Phillips, I think Griffiths is right up there.
‘Butland was playing for England before long after being at Cheltenham and I think Griffiths has the chance of playing for England.
‘But he needs to keep on playing and improving, but his attitude tells me he can get there.’