The News understands Danny Cowley remains an admirer of Griffiths who he was trailing last summer, as supporters get ready for business to accelerate.
Meanwhile, veteran striker Danny Hylton has also been mentioned as a potential target as the Blues boss aims to bolster his attacking line-up.
Today marks the opening of the window which means clubs can now begin registering players and completing deals which have been put in place.
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Griffiths is a player Cowley is still keen on, with the Londoner looking closely at the West Brom man 12 months ago.
In the end, he opted for Manchester City’s Gavin Bazunu who proved a runaway success.
But Griffiths made his own strides following a fine campaign as Cheltenham won League Two, with 35 appearances at Lincoln before an ankle injury curtailed the 20-year-old’s season in March.
The England under-18 international still has three years to go on his deal at The Hawthorns, but looks set to be sent out on loan with the Baggies tying Alex Palmer and David Button down to new deals.
And Cowley is firmly on his trail with the Pompey boss leaning towards bringing in a new keeper, with Alex Bass and youngster Toby Steward in his ranks.
Hylton is a new addition to a lengthy list of attacking names being mentioned this summer.
League One rivals Charlton and Ipswich Town are also reportedly looking at the 33-year-old, as he becomes a free agent after six years at Luton Town.
Hylton scored four Championship goals from 19 appearances last term, and has bagged 62 efforts from 170 outings in his time at Kenilworth Road.
Pompey, of course, don’t have a senior striker contracted next term with the attacking department requiring major surgery.
Marlon Pack remains a target, with Cowley keen on adding one more experienced and defensive-minded player to his midfield ranks.
Supporters will be hopeful of some quick business being confirmed in the coming days.
A limited number of deals have been announced to date across the EFL, with clubs not being able to officially register players until today.
The Blues have confirmed new deals for Sean Raggett, Michael Jacobs and Reeco Hackett, however.
That means Cowley currently has 17 players contracted for next season, along with four first-year professionals or third-year scholars.