Rangers had a £400,000 bid for the 21-year-old defender turned down last week.
If Edmundson doesn’t move elsewhere, Rangers boss Steven Gerrard could sign him on a pre-contract in January.
That would be as he goes into the last six months of his deal, although Oldham would still be entitled to training compensation.
Aside from Rangers, Wigan and Hull, Peterborough, Stoke and Derby have been sniffing around Edmundson.
Rangers transfer blow as Oldham knock back fresh George Edmundson bid - EXCLUSIVE (Image: GETTY)
Rangers transfer blow as Oldham knock back fresh George Edmundson bid - EXCLUSIVE (Image: GETTY)
Rangers have already agreed deals to sign Jordan Jones from Kilmarnock and Jake Hastie from Motherwell.
There is also a deal in place to sign Greg Stewart from Birmingham City, while the Light Blues still maintain an interest in Hearts’ John Souttar.
Meanwhile, Rangers striker Kyle Lafferty has distanced himself from reports linking him with a move to Apollon Limassol.
The Northern Irishman will have talks over his future on his return from holiday after falling out of the first-team picture.
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