Reports have suggested the 30-year-old could be on his way back to the Riverside Stadium after Spurs manager Harry Redknapp revealed he would let him go out on loan to regain match-fitness.
"It's news to me - we will wait and see what January brings," Mowbray said.
"Anybody who takes Woodgate would expect him to play and whilst (David) Wheater and (Matthew) Bates are here it would be difficult for me to bring in a loan player and disappoint one of our own players. Loans are always difficult.
"It's not something at the moment that I'm working on, but I know Woodgate was a big success as a player here."
Woodgate would be seen as an ideal replacement for David Wheater, who added to his growing stock with the third goal in Boro's 3-1 victory at bottom club Preston today.
The 23-year-old will be out of contract at the end of the season and Mowbray did little to quash reports of a January move away from the club.
"Wheater is on everybody's lips at the moment. He scored again and it was another super performance from the young man," he added.
"Wheater is too valuable an asset for us to let him walk away on a free in summer. We are in a situation which isn't ideal because you can see the connection he has with our supporters.
"Let's wait and see what January brings."
Leroy Lita scored twice as Boro secured only their second away win of the season at Deepdale and Mowbray was relieved to secure a much-needed three points.
"I'm pleased with the win of course, I think there was enough good play in there to warrant it," said Mowbray.
"We must give them a lot of credit; they didn't look like a team that was bottom of the league and they played some nice fluent football and created some chances.
"But when the game went on they had to chase it and they looked more vulnerable and disheartened and we could have scored a few more at the end.
"It was a professional performance from us in a game we needed to win, we came here and did the job."