Spurs have been tracking Gray since the start of the season, and they have stepped up their interest in the last month.
Mitchell reportedly visited St. Andrews in November to get a first hand view of the England youth international.
Gray has established a reputation as one of the finest talents outside the Premier League, and he is believed to have a bright future at the top level.
The 19-year-old has already made more than 75 senior appearances for Birmingham, and he is currently playing a key part in Gary Rowett’s team.
Birmingham are said to be willing to listen to offers in the region of £3.75 million, and Spurs believe that price is fair.
The Lilywhites are reportedly unlikely to make a move for Gray in January, but they could bid in the summer transfer window.