The 22-year-old, named in Japan's squad for the World Cup in South Africa, is expected to sign a three-year contract with the Bundesliga runners-up.
Uchida told reporters on Thursday: "I can't talk about it."
Kashima Antlers' technical committee chief Mitsuru Suzuki told the Nikkan Sports newspaper: "It will be decided soon."
Schalke had no comment on the reports when contacted by Reuters.
The Japan right-back, who has been capped 31 times and is likely to start at the World Cup, which kicks off on June 11, is expected to sign for Schalke within the next two weeks.
Uchida, a poster boy for football in Japan, will formally become a Schalke player from July 1 following completion of a medical, the media reports said.
Financial terms have not been disclosed but local media reported Uchida would earn around $2.3 million a year, a record for a Japanese player.
Schalke finished runners-up in this season's Bundesliga behind Bayern Munich.
"The reason for wanting to sign (Uchida) was to acquire a quality full-back," Schalke head coach Felix Magath was quoted as saying in the Yomiuri-affiliated Sports Hochi.
"At the same time it's hard to get full-backs like him who when they get the ball look to the forwards first or look for the goal like him."
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