Reports in several papers on Wednesday claimed that Mel was battling to save his job as Albion boss after just six weeks in charge at the Hawthorns.
There have been reports of training ground bust-ups and senior squad members are also rumoured to have fallen out with Mel's assistant Dave McDonough.
West Brom are without a win since Mel took over in January and are currently just one point outside the relegation places.
The 50-year-old Spaniard has only been at the club for 44 days and has been in charge for six games without a win - Albion drew 1-1 against fellow Premier League strugglers Fulham on Saturday which was the club's fourth consecutive home draw under Mel after going behind.
The club's sporting and technical director Richard Garlick later made a statement regarding the speculation about Mel's future.
It read: "At present, we are going through a period of transition, which is natural following the appointment of a new Head Coach.
"There is also a lot of frustration at our league position and run of form. I would be more concerned if there wasn't.
"Various meetings have been held within the football department over the past few days to discuss our current situation and what needs to be done to improve results in our final 11 games.
"The discussions have proved constructive. There has been a lot of soul searching and it is clear everyone has a real hunger and desire to keep the Club in the Premier League.
"Pepe, the coaching staff and players will now do everything in their power to achieve this common goal."