The 25-year-old has produced some impressive displays in the Barclays Premier League to help Paul Lambert's men close in on safety. Ruddy - who had a five-year spell at Everton from 2005 to 2010 after joining from Cambridge, but made just one first-team appearance - is on the radar of England goalkeeping coach Ray Clemence.
Woods - capped 43 times by England - is on the backroom staff at Goodison Park and worked with Ruddy during his time on Merseyside. Woods said in the Eastern Daily Press: "I am not surprised with John's success at all - he was with us for a number of years and he's always had great potential."
He added: "He's a great reader of the game, a great presence and he's just proved to everyone how good a keeper he has become.
"John has only played in the top flight for one season and he's not even completed that yet - but all John has got to keep doing is carrying on putting the performances in and let everything else take care of itself."
Everton head to Norwich on Saturday, and Woods added: "You know what it's like. As soon as you start playing well people start saying this, that and the other.
"You need to keep focused on the position and the job that you've got in front of you and I'm sure John will do that."
Source: PA
Source: PA