The centre-back is in talks with the Tractor Boys ahead of a move to the League One outfit.
Edmundson has fallen down the pecking order at Ibrox having broken Covid-19 regulations alongside Jordan Jones last year. In January he joined Derby County on loan, playing eight times.
With Nikola Katic returning from injury, Steven Gerrard has an abundance of centre-back options, including Filip Helander, Leon Balogun, Connor Goldson and Jack Simpson.
According to the Daily Record, Ipswich are confident of landing Edmundson, who was signed for £800,000.
The deal for the 23-year-old could see the £1million fee grow if he helps the Suffolk side win promotion to the Championship.
The Northern Irish winger spent the second half of last campaign on loan at Sunderland.