The 51-year-old was appointed by the Baggies on an 18-month contract in January and despite winning just three of his 17 games in charge, he guided them to Premier League safety.
After watching his side slip to a 2-1 defeat at home to Stoke City in the final game of the season, Mel received a warm reception from supporters during the lap of appreciation at full-time.
The Spaniard is set to meet with chairman Jeremy Peace to discuss what lies ahead after recent reports had linked him with a return to his native Spain.
Asked if he was waving goodbye to the home fans, Mel told Sky Sports: "I don't know. This week I have a meeting. I'm going to have a meeting but I don't know.
"I enjoy West Brom, I enjoy the club. I enjoy the people of West Brom because they are always very, very kind with me."
Asked if he would like to stay, he replied: "Yes of course. But I think it's very, very important for West Brom to learn from the mistakes of this season.
"I need to listen to the chairman what is the way for next season."
A late strike from Charlie Adam consigned the Baggies to defeat on the last day of the season, after Stephane Sessegnon had cancelled out Gareth McAuley's first-half own goal.
Albion finished the campaign in 17th place - just three points above the drop zone - and Mel admitted his relief that it was all over, saying that their fans played a large part in securing their safety.
"I'm disappointed because it's the last match, but the end of the season is good. For me, it is good too," he said.
"It's been an unbelievable four months for me. There's been a lot problems but everybody in the club has helped me for my work. The supporters are the best at this club.
"It's been a lot of work every day at the training ground. It was a difficult situation but the players worked together with hard work - the technical staff and the supporters too.
"For me, the supporters have made this situation possible now to stay in the Premier League."
Meanwhile, Ben Foster thwarted Jonathan Walters with an impressive save in the opening stages and Mel believes the goalkeeper is a certainty to make Roy Hodgson's World Cup squad.
"I think that Ben Foster is a very, very good player and a very, very good person in the changing room. I think England need a keeper, there's no problem," he said.