Burke has struggled to find his feet at Albion since his £15million arrival from RB Leipzig in the summer of 2017.
He has managed just a single senior goal from 24 appearances for the Baggies, and has only started two league games.
Albion will be able to recall Burke in January, should they wish to.
This will be the second time the Baggies have allowed Burke to depart on loan. He previously made a temporary move to Celtic last season, scoring four goals.
"It’s probably going to be done today," said Bilic. "He’s going on loan there, he needs minutes.
"He improved a lot – I spoke to him – in his concentration. That reflects on finishing and everything. We have good numbers there.
"We haven’t given up on him, it's basically like Sam Field and Jon Leko [who have joined Charlton on loan].
"It will be much easier to say 'listen, you’re staying here to cover ourselves', but it’s a bit too selfish.
"I expect him, Leko and Sam to go and pick up minutes, play week in week out and to come back here and play here.
"That will be for the season but I think we can recall him in January."
Spanish sides have until September 2 to complete their transfer business, with their deadline extending well beyond that given to Premier League and Championship clubs.