The Baggies have identified Cifuentes as one of their top managerial targets after surprisingly sacking former Sunderland and Middlesbrough boss Tony Mowbray last week.
Cifuentes’ representatives are said to have held talks with Baggies, and QPR have now responded by placing the manager on gardening leave.
In a statement, the club said: “Assistant coaches Kevin Betsy and Xavi Calm will take charge of first-team affairs on an interim basis and prepare the squad for our final fixture of the 2024/25 campaign against Sunderland.”
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QPR’s chief executive Christian Nourry said: “This is naturally a disappointing situation for everyone concerned.
“I fully understand and appreciate supporters’ frustrations at this time.
“As a club, we are working to ensure this matter is resolved as swiftly as possible so we can start preparations in earnest for the future.”
Cifuentes was appointed at Loftus Road in October, 2023, when Rangers were rock bottom of the Championship and six point adrift of safety.
He did a superb job in his first season in charge in guiding QPR to comfortable survival and attracted interest in the process, with Sunderland having identified the 42-year-old as one potential target as they searched for a new manager last summer.
Cifuentes ended up staying at Loftus Road but this season has been a troubled one in west London, even though he has again ensured Rangers were dragged into relegation trouble.
Again, Cifuentes has interested other clubs and West Brom made their move after sacking Mowbray last week.
That led to QPR’s gardening leave announcement on Tuesday night.
Cifuentes signed a new long-term contract at QPR last September so the Baggies would have to pay compensation for the Spaniard’s services.
QPR are 15th in the Championship table and head for Wearside on Saturday having won just two of their last 12 games. They were thumped 5-0 by Burnley last time out, after which Cifuentes was defiant.
He said: “It doesn’t define what this team has done this season and it’s very sad to finish (the season at home) that way.
“It hurts my heart because we had the desire and expectation of a much better performance.”
Quizzed at that stage about the West Brom interest, he said: “I said before that as long as I’m wanted, I’m very happy.
“In any case I am very calm about the job I have done and the fact that we have achieved what were difficult targets.
“I’m an ambitious person in the sense that I always push myself. I always want to improve.
“I have a contract and I want to keep improving. I enjoy my job here, enjoy English football, and am ready for more.”
Sunderland are looking to bounce back from four straight defeats as they aim to head into the play-offs on the back of a positive result against QPR.