Albion are winless since the Spaniard succeeded Steve Clarke at the Hawthorns and lie just a point above the Barclays Premier League's relegation zone.
That has led to meetings behind the scenes but the club stressed a change at the top is not on the agenda.
Sporting and technical director Richard Garlick said in a statement on the club's website: "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."
Matej Vydra's fortuitous late equaliser earned the Baggies a point against Fulham on Saturday, their fourth 1-1 scoreline in Mel's six games in charge.
The previous three came against Everton, Liverpool and, most impressively, Chelsea, but defeats to Aston Villa and Crystal Palace have dented their momentum.
Albion conceded seven goals in those two games and have not kept a clean sheet since New Year's Day, when they beat Newcastle 1-0 - also their last win.
Their next game is on March 8 at home to Manchester United - whose manager David Moyes has also been the subject of speculation over his job security.
They then travel to Swansea and Hull before facing two more teams in the wide-ranging fight for top-flight survival, Cardiff and Norwich.