He added: “Being made to stay beyond this summer will only tarnish four wonderful years at this incredible club and so I ask Brentford’s owners and directors to now honour their promise to let me leave in the final hours of the window.”
BBC Sport reported in July that Wissa flew home early from the club’s summer training camp in Portugal after making clear he wanted the move to Newcastle.
Ever since he has been in a stand-off with the club over his intention to join Eddie Howe’s side.
He did return to first-team training for a short period but has gone back to working away from Keith Andrews’ squad.
Wissa, who scored 19 goals in the Premier League last season, also removed all association with Brentford from his Instagram account.
In his statement, Wissa says he held “open discussions” with the club’s senior management earlier this summer about his intention to leave and said he was told the “club would not stand in my way if a reasonable offer was received. This was also put in writing”.
He says a formal offer was submitted by another Premier League club and he was “under the impression, from all my conversations with Brentford, that there was a mutual agreement to part ways”.
He added: “I want to make it clear that I have not acted unprofessionally, nor do I wish to leave Brentford on bad terms. I have been transparent in my position throughout. I have continued to communicate openly with the club and conduct myself in a way that reflects my values as both a footballer and a human being.
“I remain hopeful that a fair and reasonable resolution can still be found before the transfer window shuts.
“In the meantime, I must do what I feel is right for my career and family and insist that Brentford honour their promise to let me join a new club and at a fair price.”
BBC Sport has contacted Brentford for comment.
Watch all your favorite Amazon Prime Video Sports broadcasts live and free. Get access to NFL, NBA, NASCAR, WNBA, and more – all included with your Prime membership!