Moore is keen to bolster his squad before the start of the League One season and has identified the goalkeeping department as an area that needs strengthening.
Keiran Westwood is set to leave the club at the end of the month, while Cameron Dawson and Joe Wildsmith have struggled to impress the Owls boss.
As Sheffield Wednesday continue their search for a new goalkeeper, West Brom’s 19-year-old custodian Griffiths has emerged as a target for the Owls.
However, Portsmouth and Lincoln City have also been credited with an interest in the goalkeeper, who has been linked with a return to Cheltenham Town following a successful loan spell.
While the West Brom youngster has attracted significant interest, the Owls may have a trump card over Portsmouth, Lincoln and Cheltenham in the chase for him.
Sheffield Wednesday boss Moore has good connections with West Brom, who he represented both as a player and manager, and could leverage that relationship to land Griffiths.
The teenage goalkeeper made 50 appearances across all competitions for Cheltenham last season, keeping 23 clean sheets in the process.
