Beattie has fallen further down the pecking order following the loan arrival of Luke Moore and has now been given permission to seek a short-term move.
"It is something I have spoken to Craig about. He wants to play, and I brought him here to play, but the way things have unfolded he has found himself not even on the bench," said Mowbray.
"If Craig wants to get some game time then I am happy to facilitate that for him. I am sympathetic to his frustrations.
"There has to be a team who wants Craig. He has to want to play for that club and I've got to allow it to happen."