The non-league club have held firm despite advances from the Championship club for their 20-year-old attacker.
Archer has been impressive for the Pitmen in the Northern Premier Laegue this season, scoring a stunning solo goal against Whitby Town a few weeks ago that first grabbed Albion's attention.
He also netted in Saturday's 3-1 FA Cup victory at Rugby Town.
However, he is under contract with the Pitmen until January 2020 and they have turned down the Baggies' bid to take him on trial.
It is believed the Keys Park side want a fee for the highly-rated 20-year-old, who can play as a centre forward or out on the wing.
But the Baggies are unlikely to make an offer.
Hednesford have a history of producing high-quality players – Arsenal's Cohen Bramall, Stoke's Ashley Williams, Wigan's Chey Dunkley and Blackpool's Curtis Tilt have all played for the club.