The Sun says Woodgate is facing the sack following a very disappointing start to the season, which has seen Middlesbrough win just three times in the Championship.
Warnock is reportedly waiting in the wings to take over at Boro - who were thrashed 4-0 by Leeds on Saturday afternoon at Elland Road.
The former Crystal Palace manager stepped down at Cardiff last month after more than three years in charge.
The 71-year-old was appointed in October 2016 with Cardiff second from bottom in the Championship before he guided them to the Premier League in 2018.
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