The 27-year old would have been out of contract in the summer and Wanderers were keen to extend his current deal amid reports of interest from Premiership rivals Tottenham Hotspur.
Davies will meet with his agent this week to discuss the small print of the contract, but the Yorkshireman expects no problems as he looks to extend his stay with the Trotters.
"Hopefully it will all be sorted out by the middle of the week, I'm meeting with my agent and the people here and, hopefully, it will be done before the next game."
"Everyone knows I'm happy here and there's no question of me going anywhere else. It's just a question of fine tuning a few things and I'll be happy."