Edwards scored or assisted 12 goals in 33 games for Peterborough last season, attracting interest from Nottingham Forest, Bristol City and Ipswich Town, HITC Sport understands.
But according to the Daily Mirror, Blackburn can now be added to Welshman's list of suitors.
Edwards is set to enter the final year of his contract, although Peterborough are working on a new deal for the 25-year-old, according to their owner Darragh MacAnthony.
Working on new deal for Gwion but of course there is interest in him as expected. Doing our best on this one. https://t.co/ITJ9d1phxA— Darragh MacAnthony (@DMAC102) May 15, 2018
Worryingly for Posh, he is not the only key player linked with a move away from London Road, with teammates Marcus Maddison and Jack Marriott also said to have attracted interest from higher division clubs.
Blackburn have already returned to League One - the division from which they gained promotion last season - to sign Oxford United's Joe Rothwell this summer.
Would Edwards be a good addition for Blackburn?