HITC Sport understands Crawley winger is target for two League One clubs.
Edwards is out of contract at Crawley this summer and he has yet to agree a new deal at the League Two club.
News of his availability on a free transfer has alerted a number of clubs higher up the football pyramid with MK Dons and Charlton both admirers of the winger.
Edwards scored eight goals for Crawley last season and was one of their rare bright spots in a disappointing season for the club.
The 23-year-old came through the ranks at Swansea, but failed to make a senior appearance for the club.
The former Wales Under-21 international initially joined Crawley on loan in March 2014 before making the move permanent later that summer.
Crawley are reluctant to lose Edwards this summer, but are resigned to him moving on as they have been unable to agree a new deal with the attacker thus far.
MK Dons and Charlton are both looking to reshape their squads for next season after suffering relegation from the Championship this term.