The Wales defence coach, who recently left London Wasps by mutual consent, is now out of contract with the Welsh Rugby Union and is being touted for a position within the England set up.
The WRU are keen to keep Edwards on board, however, and Cardiff Blues chairman Peter Thomas believes a part-time role with his region would be the perfect fit for club and country.
"I would very much like him to come to the Blues," said Thomas, who lost Dai Young to Wasps in the summer and currently has Justin Burnell and Gareth Baber in charge of the capital-city outfit.
"I've spoken to the Welsh Rugby Union and registered a very strong interest in Shaun Edwards coming in to do a defensive role. He would work alongside both Justin and Gareth.
"I know Warren Gatland would not have a problem with it and I've asked the Welsh Rugby Union to give it very serious consideration.
"We wouldn't have a position full-time at Cardiff Blues for Shaun Edwards and he knows that and he doesn't want that. We have a forwards coach, we have a backs coach - we want a defensive coach. And the coaching structure of these games is that you do two, maybe three sessions a week."
Edwards has yet to voice his opinion on where he sees his next professional role but he has agreed to continue helping Cambridge University ahead of the 130th Varsity Match next month.
The 45-year-old, who was an assistant coach to Sir Ian McGeechan when the Lions toured South Africa in 2009, has been involved in the Light Blues' Varsity preparations for the past eight years and will continue to visit Grange Road in the lead up to the December 8 clash with Oxford at Twickenham.
"Shaun will definitely be with us again this year. He was going to come up for a session last week, but we had only 10 fit guys so it wasn't worth it," said Cambridge head coach Tony Rodgers.
"We've had him for eight years and the boys love him. He is terrific, but the players are all terrified of him.
"He will come up and do two or three sessions and watch a few games in the build up to the Varsity Match. I know that teams are queuing up to sign him and I'm sure Wales won't want to lose him.
"He really is something special and a true legend in rugby league. If we can get him for three sessions I know he will galvanise the players."