The Portuguese has put pressure on the Red Devils hierarchy in recent weeks to match the spending of Manchester City.
Mourinho claimed that £261m spent so far by United since taking charge at Old Trafford is not sufficient, prompting talk of a rift between the two club figureheads.
According to The Mirror, the United boss has told Woodward that he has no intention of walking out on a contract that would still have two-and-a-half years to run if the club takes up a 12-month extension option.
In response, Woodward is believed to have promised Mourinho a £120m package to sign Alexis Sanchez from Arsenal as well as full backing of the former Chelsea boss in the upcoming transfer windows.
United currently sit second in the Premier League table on 47 points, 15 behind leaders Man City.