Bridges joined The Magpies until the end of the season, when his contract with Leeds is due to expire anyway.
"Michael expressed a wish to leave the club. He felt he was going a little bit stale at our club," Eddie Gray told BBC Radio Leeds.
"But we wish Michael all the best and hope things work out for him."
Bridges scored 22 times in his debut season but has struggled to recapture his best form since because of a host of injuries.
The 25-year-old made the Leeds starting line-up just once this season with five substitute appearances.
Toon scout Jack Hixon, who discovered Alan Shearer and Bridges, today backed him to beat his critics and become a success with Newcastle.
"Cream will always rise to the top," said Hixon in the Newcastle Evening Chronicle.
"I've heard all the talk that Michael is injury-prone and not fit but it simply isn't true.
"He's had two serious injuries in his career that have unfortunately taken a huge chunk out of it. He hasn't been injured time after time with different niggles and knocks.
"And since August 1st he's been as fit as a fiddle, dying to get going again. Now he can at Newcastle and he hasn't just got a month to prove himself but three months. That's enough time for Bridges to prove to everybody what he can do."