"The manager [Sven] always asks me how Woody is when I'm with the England team, even when he was injured," Beckham said. "So I don't think he is ever out of his thoughts.
"If he saw him tonight and Woody gets a run in the team now, there is every chance of him being picked for the England team because he is more than good enough," he said.
But Woodgate, 25, is keen to keep his feet on the ground: "First and foremost I have to keep my place here and I'll train my bollocks off every day to get fitter and sharper and if I do that hopefully then I'll play more games."
Woodgate returned to action last month after 17 months on the treatment table because of a career-threatening thigh injury, but he had a horrific debut in his first La Liga match against Athletic Bilbao, scoring an own goal within 25 minutes and being sent off in the second half.
Two weeks later he suffered a minor ankle injury and followed that up by bundling into his own net in a friendly against Zaragoza.
But on Wednesday that all changed when he met a David Beckham free-kick with a bullet header three minutes into the second half to cancel out Rosenborg's shock first-half strike.
The goal acted as the catalyst to a spectacular recovery from Real, which came courtesy of a classy finish from Raul, a header from Ivan Helguera and a trademark free-kick from Beckham.
But if it was Woodgate's night, it was another outstanding performance from David Beckham that had the Spanish media drooling.
"Beckham is in a state of grace," said best-selling sports daily Marca. "He has made a spectacular start to the season." Rival AS was even more fulsome in its praise. "Beckham was majestic," said Juanma Trueba. "His goal was the icing on the cake of yet another formidable display."Reuse content