The 36-year-old had the option to continue his career in the Premier League three years ago, but preferred a move to the Bundesliga
The experienced decided to leave Madrid after he was no longer guaranteed first-team action and had several options to continue his career, including the Red Devils.
However, then Schalke coach Felix Magath eventually convinced him to sign for the Bundesliga outfit.
"The first decision was to leave and the second whether to leave to still compete at the highest level or not. He chose the latter and there were a few clubs where he could compete for trophies, including Manchester United," Carvajal told Marca.
"But there was one person – that was Felix Magath – who convinced him to go and play for Schalke.
"The United thing was serious, but there was also some uncertainty surrounding his role in the team – whether he was going to be a key player or a substitute. He might as well stay at home if he would end up at the bench.
"If he was just going to go and learn English, he could have stayed at Real. It was Magath who came to Madrid to convince him to join Schalke."
Raul left Schalke for Al Sadd in 2012 and briefly returned to Real Madrid this week for a friendly game between his current team and his former club.