Rangers have had a second bid for George Edmundson turned down by his club Oldham Athletic, according to the Daily Record.
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The Light Blues initial offer of £400,000 was rejected outright by the League Two side.
They have since returned with a second bid of £500,000 plus potential add-ons, though this has received the same response.
Oldham are said to be desperate to get close to the £1 million mark for the centre-back, who was included in the League Two Team of the Year.
This is despite Edmundson submitting a transfer request as he angles for a move to Ibrox.
Wigan Athletic and Hull City are also said to be interested.