Leeds have tried to stave off interest for last year's Championship top scorer by offering Wood a new three-year contract with an increase on his current wages of £15,000 a week,
Burnley need to bolster their attacking options following the departure of Andre Gray to fellow Premier League club Watford and they have identified the 25-year-old as an ideal replacement.
The New Zealand man netted 30 times in all competitions last year and so has attracted a lot of interest from elsewhere.
Wood managed 27 goals in 44 Championship games last term and is already off the mark for this year, scoring in the 3-2 over Bolton.
Leeds have already managed to tie down midfielder Eunan O'Kane and defenders Gaetano Berardi and Liam Cooper to new deals but it is looking unlikely Wood will follow suit.
After narrowly missing out on the play-offs last season, the Yorkshire club are targeting promotion this time round but would struggle to replace Wood's goals.
They have lined up loan deals for Pierre-Michel Lasogga from Hamburg and Ross McCormack from Aston Villa.