The 21-year-old, who is reportedly valued at £500,000, is in high-demand with the Latics already forced to reject offers for their prize asset.
Alongside the trio, Championship clubs Stoke City, Hull City and Preston North End are also credited as well as SPFL outfit Rangers.
Edmundson has undergone the same footballing education as Burnley star James Tarkowski, who also came through the ranks at Boundary Park.
Meanwhile, Sunderland are set to appoint former Celtic chief scout John Park as their new Director of Football, the Daily Mail claims.
Hoops interim boss Neil Lennon wanted Park to return to the SPFL giants after former Black Cats sporting director Lee Congerton left for Leicester City last week.
But, it is believed Park has instead opted for a move to the Stadium of Light after being offered a five-year-deal.
Park, who was chief scout at Celtic between 2007 and 2016, was credited with discovering the likes of Virgil van Dijk, Victor Wanyama and Ki Sung-yueng,
Scunthorpe United have confirmed the arrival of Paul Hurst as the club's new manager.
The 44-year-old has been out of work since being sacked by Ipswich Town in October after just 14 matches.
Hurst, after leading Ilkeston Town, Boston and Grimsby to promotion, almost took Shrewsbury to the Championship in 2018 but lost the playoff final to Rotherham.
He will be joined by former Nottingham Forest defender Chris Doig, who has taken on the role of assistant manager.
In League Two, Northampton Town have completed their second signing of the summer with the capture of Stevenage left-sided player Joe Martin.
Martin, 30, was released by The Boro last week having spent the first-half of the term on loan at Bristol Rovers.
He becomes Curle's second signing as Cobblers boss following last week's capture of Stockport County attacker Matty Warburton.
You can read the full story via the Northampton Chronicle and Echo HERE.
MK Dons have released Ousseynou Cisse and Brandon Thomas-Asante to make room for new signings, Paul Tisdale has revealed.
Cisse made 26 appearances in League Two this season to help the Dons gain promotion while Thomas-Asante spent most of the season on loan at Sutton and Oxford City.
"You build a team throughout the course of the year, Brandon and Ouss have been very much a part of that," said Dons manager Tisdale
"I can't afford to keep everybody and I also want to make one or two signings - I have to clear some room."