The 28-year-old published a statement on social media asking the Bees to "honour their promise", saying the club is blocking his exit despite “a series of fair offers”.
Wissa has been heavily linked with a move to Newcastle for much of the summer, and the player has now asked Brentford to let him leave in the last two days of the window.
"I ask Brentford's owners and directors to now honour their promise to let me leave in the final hours of the window," his statement read.
"I have stayed silent for much of the summer, but with just hours remaining of the transfer window, I feel compelled (to) make it clear that I want to leave Brentford.
"I believe the club are unduly standing in my way despite a series of fair offers throughout the summer.
"This has left me in a difficult and frustrating position. It saddens me to have to write that, and I maintain total respect for the club and its fans."
Newcastle recently had a £35 million bid for Wissa rejected, with Brentford understood to be asking for £65 million.
The Magpies are also contending with uncertainty around Alexander Isak, who has pushed to join Liverpool after a £110 million offer earlier this month.