Murray has scored 19 goals in 38 league starts for the Seagulls, and Slade has underlined his desire to keep the striker.
"There is no doubting Glenn's quality," Slade told the club's official website. "In my opinion he is one of the best strikers outside the Championship and I don't want to lose him.
"I want him to be part of my squad for next season and am not under any pressure to sell players. Glenn's statistics show he is a 25 goals-a-season forward and he will be a massive asset for us next season.
"The club made a big investment in the player when he signed last year, and although I understand his reasons for submitting a transfer request, he still has two years left to run on his contract."