Woodward walked away from the botched recruitment process following the RFU's indecision about whether the England performance director position would include influence over the England team.
The former chief executive John Steele cancelled Woodward's interview on March 17 and then decided to downgrade the position. He was ousted by the RFU management board on Friday,
Woodward has publicly pledged his commitment to the British Olympic Association through to 2012 - but is reportedly still interested in taking up the role at Twickenham.
When that was put to Thomas on Sunday, he urged Woodward to get in touch before eulogising about the qualities he would bring to the post.
"If that is the case then Clive and I need to speak. Clive knows my telephone number and I would happily speak to Clive Woodward," said Thomas.
"You have got to respect what the man has done. I accept he had an outstanding bunch of players to work with but he was the guy who plotted England's (World Cup) success in 2003.
"The detractors will say that he left the union (in 2004) in unfortunate circumstances, that he was critical.
"It was a disagreement with Francis Baron, our previous chief executive. Like divorce it was six of one, half a dozen of the other. Clive has held his hands up to that.
"He had a disastrous Lions tour, OK. He has acknowledged that. It is over. He went to soccer to expand. He has been at the BOA and there has been nothing to blot his copybook at the BOA.
"This guy has a unique set of skills. He not only understands rugby at the elite end but he has developed a talent for sporting success across a variety of disciplines. You have to see him."
It has been suggested that Woodward could initially take the RFU position as part of a job-share arrangement with the BOA, where he is also performance director, before moving full-time into Twickenham after the Olympics.
But Thomas scotched that notion and confirmed Woodward would have to quit the BOA if he wanted to return to the RFU, seven years after storming out after a row with former chief executive Francis Baron.
Thomas believes Steele has already wasted enough time over the appointment and he is determined to fill the position after the 2011 World Cup.
"The England rugby team and its success is critical to me," said Thomas.
"We languish at sixth in the IRB rankings. It is unacceptable.
"I don't believe we can have a situation where we have a part-timer doing the job even if he was to come at a later stage. That for me would not be an answer.
"We need a man that has a skill set that is 100% committed to putting England back to where they need to be.
"We need success in New Zealand and that is totally down to Martin Johnson and his coaches and we then need to be looking forward to 2015, which may sound a long way away but it isn't.
"The RFU job is a full-time job. We have already lost a lot of time."
With regards to the RFU chief executive, Thomas said he had already spoken to the recruitment consultants he wants to engage to find the right man.
Thomas is the acting chief executive and he would not rule out a temporary return to the RFU for Francis Baron, whose business acument established the union as the most commercially successful in the world.
"We will look at any applicant but I wouldn't rule it in or out," said Thomas.
Simon Halliday, a former RFU councillor, and Malcolm Wall, who was beaten to the post by Steele, have both been mentioned as potential candidates for the full-term post.
Wall, who took over as chairman of Harlequins following Bloodgate, has recently taken a role with Abu Dhabi Media.
The RFU board had agreed earlier this year to appoint a non-executive director. Steele had wanted an individual with a sporting background but Thomas favours a financial heavyweight from the City.
The RFU are due to post projected losses of £11million this year because there are no autumn internationals and only two home games in the Six Nations.
"John has a view that we needed to bring in someone from the Olympic environment," said Thomas.
"I think we face a difficult time at the moment. We will obviously post significant losses in the next few days. It is where we are in this wretched four-year cycle.
"I have a concern that we have to watch the financial side of things.
"We have to try and balance an understanding and empathy with rugby and a greater financial expertise than we were looking at with John.
"My idea is we have to look for a serious heavyweight financial person from the City, who will sit on the board, with particular financial expertise."
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