Hoops boss Ange Postecoglou has already bolstered his squad in this window but is keen on further additions, with midfield a priority.
Postecoglou zeroed in on Dons star O’Riley and Celtic have been working on getting a deal over the line for him.
And the Hoops are now close to striking a deal with the League One side for the 21-year-old, which will see them pay £1.5m.
O’Riley is expected to complete a move north of the border in the coming days and link up with Postecoglou at Celtic Park.
The midfielder only joined MK Dons from Championship side Fulham last January but is now set to play top flight football in Scotland.
O’Riley has been one of MK Dons’ standout players in League One and Celtic will be hoping he will step up his game further under Postecoglou’s tutelage.
The midfielder also attracted interest from the Championship in the shape of Blackburn Rovers and Swansea City, but Celtic have now won the race for his signature.
