Aitor Karanka’s men currently sit on top of the Championship table, but they are determined not to rest on their laurels.
Middlesbrough are keen to strengthen their group in January, and Davies is one of the players on their wishlist.
Bolton are likely to have to cash-in on some of their key stars in the new year, due to the financial struggles they are suffering, and Davies could be sacrificed.
Middlesbrough reportedly feel he could enhance their midfield ranks, and strengthen their bid for promotion.
Davies has been with Bolton since 2009, and he has previously shown his ability to play in the Premier League.
The 27-year-old has suffered with a series of injuries, but his talent has never been in doubt.
Davies has played 19 times for Bolton this term, but he has been unable to guide Neil Lennon’s side away from trouble.
If Davies does move to the Riverside, he will be in competition with the likes of Grant Leadbitter and Adam Clayton for a spot in Karanka’s team.