The ex-Leeds and Newcastle centre-half has been dogged by injury since his move to Real Madrid two years ago and has made only ten starts for the Spanish giants.
Boro are thought to be after Woodgate on loan for the season, after Sylvain Distin pledged his future to Manchester City.
There is no question about Woodgate's talent, having played for England on five occasions, but there is that worry over his fitness and his ability to last the season out.