HITC Sport understands Middlesbrough are closing in on striker deal.
New Middlesbrough manager Garry Monk
Middlesbrough have been tracking for Miller for some time after he burst onto the scene with Bury last season.
The 18-year-old is regarded as one of the best young talents in the Football League following his goalscoring exploits for Bury.
Miller started only five games last season with most appearances coming off the substitutes bench, but he still managed to score eight goals for the Shakers.
General view of Middlesbrough's Riverside stadium
Scouts from Premier League and Championship clubs have been keeping tabs on Miller, but Middlesbrough have firmed up their interest by making a bid for his services.
Bury have been reluctant to lose one of their prize assets, but they have accepted Middlesbrough's offer for the player.
Middlesbrough are understood to have agree a fee in the region of £200,000 plus add-ons with Bury for Miller with the player having a medical on Teesside today.
If Miller seals his move to Middlesbrough he will become Garry Monk's third signing at the Riverside following the arrivals of Jonny Howson and Cyrus Christie from Norwich and Derby respectively.