The 19-year-old won the League Two title with Cheltenham this season during an impression loan spell from the Baggies.
The Premier League club are keen to once again send out the highly-regarded Griffiths in the 2021-22 campaign to aid his development.
Griffiths has come through the ranks at The Hawthorns and featured for England under-18s, while was part of the Three Lions’ squad at the 2021 European under-21 Championships.
He made 50 appearances for Cheltenham this season, missing just two league fixtures, as they claimed the League Two crown.
A return of 23 clean sheets helped him collect the Robins’ Young Player of the Season trophy before returning to his parent club.
Cowley has drawn up a shortlist of candidates to bring to Fratton Park, with Griffiths featuring highly.
However, it is understood West Brom are only interested in a loan for the stopper, who is seen as a potential first-team keeper at The Hawthorns.
Alex Bass is presently the sole keeper on Pompey’s books as Cowley seeks to overhaul a playing squad which finished eighth.
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