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 on Tuesday.
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, saying: "Wheater is on everybody's lips at the moment. He scored again and it was another super performance from the young man. Let's wait and see what January brings."
Source: PA
Source: PA