The 23-year-old has only started three Premier League games for the Magpies this season.
The Baggies are keen to bring him in to replace Harvey Barnes, who was recalled by Leicester earlier this month.
Like Barnes, Murphy is a young, versatile forward capable of playing on either wing or as No.10.
He joined Newcastle from Norwich in the summer of 2017 for an initial £10million.
Murphy has pedigree in the Championship, having scored 10 goals and laid on nine assists from 46 appearances in the second tier.
"We are trying to improve the squad," confirmed Darren Moore today. "We’ve been talking to bring players in.
"The players we’ve identified we feel will help the squad and benefit the team.
"It’s a lot harder than me just speaking because there’s a lot of things to go through.
"But we’re working extremely hard to improve the team and get a few more bodies in because at this time of year, like anyone else, you get knocks, injuries and suspensions.
"It’s important we strengthen if it’s possible to do so."
Albion already have Dwight Gayle on loan from Newcastle and while Premier League clubs are not allowed to loan more than one player from the same club, EFL clubs can.