"In contrast to others who just do it via the media, I personally called Mr. Blatter some time ago and urged him to resign," Rauball told this week's Kicker magazine.
Rauball did not say what Blatter's response was. He has been a vocal critic of Blatter on the issue of Qatar.
"I was one of the first who massively criticized the choice of Qatar," Rauball said. "However, the executive committee's decision for Qatar did not come from Mr. Blatter alone, but from the 22 eligible members."
Rauball said it would be a "Herculian effort" to find the right path of action because of the "many different interests" within FIFA and its 209 members, adding that smaller nations had a higher consideration of economic factors.
He also repeated his suggestion that UEFA leaving FIFA was "one of the options" if world football's governing body does not publish in full American attorney Michael Garcia's report into bidding for the 2018 and 2022 World Cups.