Woodgate, sold by Peter Ridsdale to Newcastle in 2003, has had two injury-ravaged seasons since moving to Madrid from St James' Park, and the Spanish club took advantage of Leeds' facilities by reaching an agreement to send him to Thorp Arch in April.
The Middlesbrough-born 26-year-old finished his training schedule alongside United's first team squad this week.
Woodgate said in the YEP: "The training's been hard, it's probably one of the hardest pre-seasons I've ever had, but hopefully I can go back to Madrid and start flying again." .
On reports suggesting that the Whites were planning to strike a deal which would see Madrid pay the bulk of Woodgate's wages, the defender said: "I don't know where that came from, it was a load of nonsense."