Woodward is believed to have expressed a desire in taking over from Saint-Andre, who is set to leave his position with Les Bleus after the World Cup this autumn, and is on an eight-strong shortlist to replace the ex-Sale and Gloucester coach.
The 59-year-old is understood to have met with French rugby chiefs last month to formalise his interest in the role and signal his interest in returning to Test match coaching.
Saint-Andre has come under fire for presiding over a record of 15 victories in 37 Tests, while his pragmatic style of play has not always been met with approval from a nation which craves a more attacking-minded and free-spirited approach.
Highly-decorated and long-serving Toulouse boss Guy Noves, who has won more European titles than any other coach, remains the front-runner for the job.
Former France skipper and Saracens and Wasps hooker Raphael Ibanez is also said to be in the frame, although Woodward’s trump card could be his experience on the international stage.
Ex-Harlequins centre Woodward led England for 83 matches between 1997 and 2004, with his crowning glory coming in 2003 when he oversaw England’s World Cup triumph in Australia.
That followed a Six Nations Grand Slam success in the same year, while he also notched 12 consecutive victories home and away against South Africa, Australia and New Zealand as England accelerated towards World Cup glory.
Woodward took charge of the British and Irish Lions’ ill-fated whitewash tour of New Zealand in 2005 before a stint as Southampton Football Club’s technical support director. He then joined the British Olympic Association in 2006, initially as elite performance director, before leaving in the aftermath of London 2012.
1994-97: Coached London Irish, Bath and England under-21s
1997-2004: England’s first professional coach. Won Six Nations and World Cup in 2003
2005: British and Irish Lions coach. Oversaw New Zealand series defeat