The Premier League club are winless in the seven games since the Spaniard took over from Steve Clarke last month and sit just a point clear of the relegation zone.
Amid reports that Mel's position at The Hawthorns could be under threat, Richard Garlick - West Brom's sporting and technical director - confirmed on Wednesday that "constructive" talks have taken place this week to try and end the slump in form.
And Garlick has backed the former Real Betis coach to safeguard West Brom's top-flight status.
"At present, we are going through a period of transition, which is natural following the appointment of a new head coach," said Garlick in a statement on the club's official website.
"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."
West Brom's next game will see them host champions Manchester United a week on Saturday.
