The Cherries will now allow defender Mings to leave the Vitality Stadium after Mepham completed his £12million transfer last night.
The Baggies are currently favourites to land the 25-year-old on loan but they face competition from Villa and Nottingham Forest.
Mings, who cost Bournemouth £8m in 2015, is a versatile left-sided defender who would provide competition for Kieran Gibbs at left-back as well as cover at centre-back.
His arrival at The Hawthorns would pave the way for Conor Townsend’s exit on loan and would allow Tyrone Mears to be released at the end of the month when his contract runs out.
However, Villa are expected to step up their interest in the defender this week, and both them and Forest may be able to offer him stronger guarantees of first team football.
Baggies boss Darren Moore has been searching for a left-sided defender this month after adding Everton loanee Mason Holgate to the right hand side of his backline at the start of January.
He is now dealing with an injury crisis in midfield, where he currently has James Morrison, Matt Phillips and Chris Brunt sidelined.
None of those players are expected to feature in the FA Cup fourth round at Brighton this weekend, a match which will see Jake Livermore serve the final game of his four-match ban.
But Moore does not believe he is short in central midfield.
“We feel we’ve got certain personnel who are adaptable and can play those positions,” said Albion's head coach. “There’s one or two that can be factored in to play there.”
As well as searching for a defender, Albion are yet to replace Harvey Barnes, who was recalled by Leicester City. But Moore insists it is not necessarily the priority.
“We’re looking to strengthen the team in all areas if possible,” said Moore. “It won’t be just in one isolated area it’s all over. If a player does become available then we’ll try to bring them in.”