Ginés Carvajal told Radio Marca that United made a "serious" offer for the star, but he chose to move to German club Schalke because Sir Alex Ferguson gave no guarantees about his role at Old Trafford.
Speaking to Radio MARCA, Carvajal said: "The first decision [Raul made] was to leave and the second, whether to go to a rival or not. He chose a rival.
"There were some offers made by rival clubs, among others Manchester United. But one person, [Schalke coach] Felix Magath, convinced him to go with him and fight for Schalke.
"The offer from United was serious, but at the same time there was some doubt about his role in the team. If you're going to play second fiddle, you might as well stay at home. For the sake of learning English, you can stay in Madrid.
"Felix Magath came to Madrid to convince [Raul]. This isn't easy for someone like him, a man who has won everything as player and coach. He negotiated with [Christoph] Metzelder [who also joined Schalke from Madrid that summer] and between the two of them they convinced him."
Raul scored 228 goals for Madrid, and at his peak was one of the most feared strikers in world football. United's former manager Sir Alex Ferguson regularly cited him as one of the best players in the world.
'Bale would make the difference'
Raul is back in Madrid this week to play in the Bernabeu trophy, a friendly tournament dedicated to the memory of Real Madrid president Santiago Bernabeu. The striker will make guest appearance against his current club, Al Sadd, taking the number 7 shirt from Cristiano Ronaldo, who has been linked with a return to Old Trafford throughout the summer.
Speaking about Madrid's possible signing of Gareth Bale, Raul said everyone at the club would be "delighted" with the transfer, adding that the Welshman would be a superb signing.
"Bale is a player who can make the difference, he has done that in recent seasons," Raul said. "Behind Cristiano [Ronaldo] and [Leo] Messi he is the player pushing up the most.
"It seems Madrid want him and will make a big effort to get him. If it happens everyone at the club will be delighted."
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