The Reds were first linked with the Schalke youngster earlier this month.
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With the February 3 deadline looming, they have been given the green light to pursue him, per Bild.
Forest are targeting Bulut to strengthen Nuno Espirito Santo's squad, with Bournemouth also interested.
Valued at €2M, Bulut could be a bargain as Schalke need to raise funds quickly.
The teenager, primarily a right-back, is under contract until 2026 and is not likely to sign a new deal.
