However, Nottingham Forest have been persistent in their pursuit of the young goalie.
They thought they had secured a deal for his services as part of a deal to bring Aaron Donnelly to Dens Park on a permanent move, only for that deal to fall through.
Courier Sport understands Graham has now agreed a move to the City Ground.
The deal with Dundee has been agreed in principle with the final aspects expected to be completed.
The Dark Blues are happy with the fee agreed and it is expected Graham will become a Nottingham Forest player in January.
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EXCLUSIVE: Dundee starlet Ally Graham set to join English Premier League outfit
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