Woodward has decided United will not be following up on their interest, if the winger sticks to his current wage demands.
Bale will only consider leaving Los Blancos if he is given wages in the region of £450,000-a-week, reports the Daily Star.
United, who already have a bloated wage-bill, are not able to meet the 29-year-old current demands and as a result will now look at other targets.
Woodward is still looking to justify his signing of Alexis Sanchez, when the Chilean was given a £500,000-a-week deal in 2018.
The 30-year-old former Gunner has only managed to score three goals in his two seasons with United and his salary is reportedly a source of discontent in the dressing room.
Although Bale would be expected to return a much higher goals to games ratio than Sanchez, the winger would also turn 30 before the start of next season.
During his five years at Madrid Bale has 63 goals in 123 La Liga appearances.
It is no secret Bale and Real boss Zinedine Zidane have not always seen eye-to-eye in the past.
And with the return of Zidane to the Bernabeu, or his second stint at the club, Bale’s future at the club has once again been cast into doubt.
Despite Bale possibly seeking greener pastures elsewhere, United don’t appear keen to stump up the £80m it would take to get the forward out of Spain.
Instead they are expected to look at younger talent in the form of Jadon Sancho, Declan Rice, as well as Chelsea’s in-demand winger Callum Hudson-Odoi.
Newly appointed permanent boss Ole Gunnar Solskjaer, also wants Marcus Rashford to agree to a long-term deal with contract negotiations expected to continue in the near future.
Another factor in the equation is goalkeeper David de Gea.
As the 28-year-old Spaniard is seeking a significant increase in his wages, after reports emerged that Paris Saint-Germain are ready to offer him a staggering £350,000-a-week if they can secure a deal in the summer.
His current deal expires at the end of next season and United are currently in a deadlock over agreeing terms on a new deal.
If no progress is made United might have to resort to selling their superstar between the sticks rather than risk losing him on a free when his contract is up.