The 32-year-old former England international is a free agent having played for Stoke last season.
And the npower Championship club have revealed on their official website, mfc.co.uk, that Woodgate is close to starting a second spell at the Riverside Stadium, where he played 52 times after an initial loan move from Real Madrid six years ago.
Boro eventually paid the Spanish giants ?7million for Woodgate on that occasion before an ?8million move to Tottenham in January 2008.
The former Leeds youngster has commanded in excess of ?35million in transfer fees despite suffering an injury-stricken career.
Source: PA
Source: PA