Baggies boss Tony Pulis is looking to add midfield reinforcements to his squad at the Hawthorns following Darren Fletcher's departure to join Premier League rivals Stoke earlier in the summer.
And 26-year-old McCarthy is believed to be back on his wanted list after there was some interest mentioned just after the end of last season.
Newly promoted Newcastle and the Foxes have also been linked, but the latter seemingly pulled out of the race after sealing a near £13million deal for Spanish midfielder Vicente Iborra from Sevilla.
McCarthy is keen to leave Goodison Park, having made just seven Premier League starts last season, while the club have been busy bringing more new faces into the club this summer.
The main obstacle to any deal taking place continues to be the price tag as Everton want up to £25 million and that could prove to be prohibitive.