Edwards has doubled up the Wasps post with his role as a part-time defence coach with Wales, and has recently returned from the World Cup in New Zealand where Wales reached the semi-finals.
Edwards moved into coaching in rugby union after a career in rugby league which saw him win a record eight championships and a record nine Challenge Cups while playing for Wigan.
Having helped Wales finish fourth in the World Cup, Edwards is understood to have attracted the interest of the Rugby Football Union, who have yet to confirm the future of team manager Martin Johnson.
Edwards' future at the club had been in doubt after he recently revealed that he expected to return from the World Cup as a "free agent".
Edwards spent 10 years at Wasps, winning four league titles and two Heineken Cups, and has been released from his Adams Park contract which had just over 18 months remaining.
With his Wales contract having expired following the third-place play-off defeat to Australia, bringing an end to a part-time role he had filled with Warren Gatland's side since the beginning of 2008, Edwards is a man in demand.
WRU chief executive Roger Lewis is known to be keen to ensure that Edwards and the remainder of Gatland's coaching set-up remain with the national side.
The RFU were due to discuss England's poor World Cup performance at a Twickenham board meeting today.
A possible outcome of the quarter-final exit to France could see team Johnson retained but his backroom staff jettisoned, opening the way for Edwards to work with England after turning down a miserly offer to work with the Saxons four years ago.
However, any rapid progress on that front may well be halted by the ongoing reviews of the red rose's tumultuous time in New Zealand.
Another potential future home for Edwards could be with the Cardiff Blues, who are without a full-time boss after Dai Young made the move to take over the director of rugby role at Wasps.
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