Striker Gray has attracted admiring glances from rival clubs after hitting 19 goals for the Bees in the latest campaign.
But Dijkhuizen hopes to hold on to the 23-year-old, who joined Brentford from Luton on a three-year deal in June 2014, and other key players from their unsuccessful Sky Bet Championship play-off challenge.
“Yes, I hope we can keep him,” said the Dutchman.
“I have a lot of quality players like James Tarkowski, Gray, Jota and also a good goalkeeper in David Button.
“We want to get better as a club and, as a team, better as well.”
Brentford are expected to be busy in the transfer market this summer, using their new statistical approach to player recruitment.
But Dijkhuizen says the current squad will have the chance to impress him ahead of the new season.
“There’s always a chance for everybody with a new coach – especially with me, I am open-minded and everybody will get a chance,” he added.
“I have no opinion about anyone. They will come in on July 1 and they will all have a chance.
“My stance is that the best players play. It doesn’t matter if they are 18 or 30, the best player plays.”