Bale has been the subject of frenzied transfer speculation this summer, with the Wales international linked with Real Madrid as well as a move to Old Trafford.
The Daily Mirror are reporting that United are prepared to spend £60m to secure his services as new United boss David Moyes attempts to strengthen his squad.
Bale scored Spurs' goal in their 1-1 pre-season friendly with Swindon on Tuesday and he remains part of Andre Villas-Boas' plans for the new season.
United chief executive Ed Woodward left Manchester United's tour of Australia earlier this week to carry out urgent transfer business - with Sky Sports understanding the deal involves a player arriving at Old Trafford.
Although it is unclear what deal Woodward is working on, he apparently told United officials of his immediate departure whilst they were at the State of Origin Rugby League match at ANZ Stadium.
Woodward was not at the game and is expected to return to Europe at some point on Thursday.
Spurs boss Andre Villas-Boas revealed earlier this summer he has been given assurances by chairman Daniel Levy that the 23-year-old will not be sold.
"The chairman said that we are not open to offers, whatever they are, and that the player will stay," he told Portuguese newspaper O Jogo late last month.
"In football anything can happen, but these are the guarantees given to me.
"There was a moment last season when Gareth came to me because he was not comfortable out on the pitch.
"I do not know if it was my response or that he was glad to relieve the stress, but after that he became confident and played with freedom. He felt important and finished the year in style."