Gilbey is currently out of favour with Addicks boss Ben Garner and has entered the final year of his current contract at the Valley.
Garner has already reinforced the middle of the park this summer with the additions of Conor McGrandles and Jack Payne, both on free transfers.
As things stand, Gilbey will be allowed to leave for pastures new, with two out of his three suitors in the Imps and the Shrews hoping to keep him in the same division.
The other alternative would be to drop down a division with the O’s.
Gilbey made 40 appearances in all competitions during the 2021/22 season, scoring three goals and recording three assists.
So far in the new campaign, the 27-year-old appeared for the full 90 minutes only once, in the EFL Cup win over Queens Park Rangers.
Gilbey was left off the bench for the recent League One games against Derby County, Sheffield Wednesday and Plymouth Argyle while staying rooted to it for the season opener against Accrington Stanley.
The Addicks wish to make further additions before the transfer window closes, but that is dependent on first moving out-of-favour players through the exit door.
