The 50-year-old Spaniard, who has had spells in charge of nine clubs since 1999, is the bookmakers' favourite for the post and one of three candidates in the running to succeed Steve Clarke, who was sacked on December 14 after 18 months in the job.
Mel was as short as 1/6 for the job with Sky Bet at one stage, although his price eased when Malky Mackay was supported for the position following his departure from Cardiff City.
Despite reports to the contrary, Mel, who counts Getafe, Rayo Vallecano and Alaves among his previous employers, did not attend Albion's 1-1 draw with Tottenham on Boxing Day.
The club refused to specify the identities of those in the frame, but confirmed via a statement on their website: "We have identified suitable candidates to work within our existing structure.
"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 tomorrow's game at West Ham United and until an appointment has been made."
Caretaker boss Keith Downing, who took charge of the team at White Hart Lane for a second time having previously secured a point from a 1-1 home draw with Hull, is likely to again be in the hot-seat for Saturday's clash against fellow strugglers West Ham.
After Thursday's match Downing insisted the delay in naming a successor to Clarke could be getting to the players but understood the board's decision not to be rushed into a quick appointment.
"There is a lot of speculation," he said. "The players have given me everything, but the uncertainty is in the back of their minds.
"The quicker they do it the better but having said that it has to be the right one.
"I have always said I would be there supporting as best I can until they make the correct one."