Campbell, who is currently on loan at Greek champions Olympiacos, played under Mel during a loan spell at Real Betis last season.
The 21-year-old Costa Rica international has yet to play in the Premier League, having joined Arsenal from Saprissa in August 2011.
However, he received a work permit to play in England last year and Mel is keen to give Campbell the chance to shine, providing West Brom retain his services as head coach.
"Joel Campbell was a player with me at Betis, a very good player and it is possible for the future at West Brom," Mel said on Friday.
"He could play here if I stay here. The most important thing now is the next three matches.
We need an extra point, sure (to avoid relegation). Arsenal, Sunderland and Stoke City (West Brom's remaining opponents) are the most important now."
West Brom have been mired in relegation trouble throughout the campaign, but a 1-0 victory over West Ham last weekend left Mel's charges four points clear of the drop zone and they have the added bonus of a game in hand.
