Mel had flown to London for talks with West Brom regarding the vacant position.
Bookmakers installed the former Real Betis manager as the favourite to replace Steve Clarke, who was sacked two weeks ago, but Press Association Sport understands he is no longer being considered for the position.
It is understood that Mel wanted to bring his own team of backroom staff to the Hawthorns, but the Baggies wanted to stick with their own coaches like Keith Downing and Dean Kiely, who have been at the club since 2011.
Mel, whose three-year spell at Betis came to an end on December 2, will fly back to Spain while West Brom consider other candidates.
Bookmakers now make Malky Mackay favourite to succeed Clarke.
Mackay's struggle with Vincent Tan ended on Friday when the Cardiff owner sacked the former Watford boss.
Although Mackay's stock is high in football, a move to West Brom so soon after a trying spell at Cardiff may be too much for the Scot.
It is also important to note that West Brom have already held discussions with several candidates over the vacant position.
Although Mel was the bookmakers' favourite, Albion never offered him the job and there were still plenty of others in the frame before he was told he was no longer under consideration.
Former Osasuna boss Jose Luis Mendilibar and ex-Liverpool defender Mauricio Pellegrino have been mentioned as possible candidates - as has Paul Clement, who is currently assistant to Carlo Ancelotti at Real Madrid.
West Brom released a statement on Friday stating that they were closing in on a new head coach.
Until that appointment is made, Downing will continue to be caretaker.
"We have identified suitable candidates to work within our existing structure," sporting & technical director Richard Garlick said.
"This is a confidential process and it is inevitable there will be speculation about whom may be under consideration.
"We are now progressing through the interview and short-listing stage. We plan to make an appointment at the earliest opportunity but our primary concern is recruiting the most suitable individual.
"We are grateful for the professional manner in which Keith Downing, the coaching staff and the players have approached the last two games.
"Keith remains in charge for (Saturday's) game at West Ham United and until an appointment has been made."
Mendilibar would be an interesting appointment for Albion. The 52-year-old guided Real Valladolid to the Spanish top flight in 2007 before spending two and a half years at Osasuna.
Downing, meanwhile, has done a good job in his two games in charge. The former Wolves midfielder has seen his men come from behind on two occasions to secure draws against Hull and Tottenham.
West Brom are three points outside the drop zone, but West Ham are two points from safety after their 3-1 defeat to Arsenal.
Downing expects the Hammers to come out fighting at Upton Park.
"We know what they are like, we know their strengths are and I am sure Big Sam (Allardyce) will have them charged up," Downing said.
"It's a big game, but we have never shied away from the position we are in and we need to get as many points as we possibly can and pave the way for the new man to come in."