United are resigned to losing the 24-year-old but Van Gaal stated that the club will not sell on the cheap, despite him being available for free next summer.
"I'm not the most important part with De Gea," said Van Gaal after the 1-0 win.
"The most important part is the player and the club who wants to buy him.
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"He's our best player for the past two or three years so we cannot let him go so easily."
Manchester United have previously rejected offers of around £13million, about £10m below their valuation of the Spanish international.
"We want to sell at the same level as we pay. We want to keep him of course," added Van Gaal.
When asked if the problem was Real Madrid not meeting United's valuation of the Spaniard, Van Gaal said: "I don't want to interfere in that because it's not the place and I think it's none of your business neither."
Sergio Romero, a free signing who joined the club less than two weeks ago, started in place of De Gea but had little to do for much of the match.
The Argentinian pulled off a crucial block to deny Walker before United took the lead and also saved two good efforts from Christian Eriksen at the death as Spurs looked for an equaliser.
Van Gaal was impressed by the 28-year-old's performance given the short amount of time he has had with the club.
"We have observed (De Gea) in preparation and that was not the same David de Gea as last year," Van Gaal said.
"Of course when the situation has been cleared after September 1 we will look again. But I'm happy Sergio did well. He saved us twice.
"We have to improve his building up, but Sergio trained only two days with his fellow players."
Additional reporting from PA
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