England's 2003 World Cup-winning coach recently left his position as the British Olympic Association's director of sport following London 2012.
Ritchie is anxious to draw on the expertise of those involved in the Olympics, but he insisted: "We don't have any vacancies. I respect totally what Clive did in rugby and the Olympics, but I am not going to get into hypotheticals. I am very happy with the way things are progressing at the moment."
The RFU are currently advertising for a head of athletic performance to work with the England team, although the job description would only cover part of Woodward's expertise.
The very fact Ritchie is in office at Twickenham is due to last year's managerial meltdown, which was sparked by a disagreement over whether Woodward should return to the RFU.
At the time, Woodward was in the frame to become England's performance director, a role that is effectively now part of Rob Andrew's brief as professional rugby director.
Ritchie not only denied that Andrew's position is under threat from the review that is being conducted into the RFU's performance department but backed his contribution to the union.
The review was proposed following England's disappointing 2011 World Cup campaign and is being conducted by Peter Keen, the former UK Sport performance director, and Sir Ian McGeechan.
"Is this a shorthand for 'what does it mean for Rob Andrew?' Certainly not," Ritchie said. "Rob has been involved in this process and supportive of it. He has great expertise.
"We should be aiming in the next three years to be giving the best possible support to the England players and the England team at all the age levels and that is fundamentally what the review is about."