Tashima announced on Thursday that he intended to run in the March election, becoming the first Japanese candidate to seek world football's top job.
The 68-year-old former Japan international has served on the FIFA Council since 2015 and became JFA president the following year before being succeeded by Tsuneyasu Miyamoto in 2024.
"I've received many messages saying, 'Thank you for speaking out'...," Tashima told Japanese daily Sports Nippon in an interview published on Sunday.
"I've been contacted by presidents and international department officials from eight countries, including some outside Asia.
"While I haven't received any formal endorsements yet, I'm getting a positive response. Since time is short and I don't want to be held up by incomplete paperwork, I want to secure support from at least six associations."
Tashima requires nominations from five national associations, a prerequisite for standing in the election.
Candidates have until November 18 to submit nominations for the election, in which Infantino is seeking a fourth term as head of world football's governing body.
Infantino came under scrutiny in July after an unsuccessful attempt to bring private investors into a new FIFA commercial entity holding rights linked to competitions including the World Cup.
Despite the criticism, Infantino's candidacy received a significant boost in October when the head of Asian football publicly endorsed him, while support from several FIFA confederations has left him well placed among the organisation's 211 member associations.
"I'll keep what's good and change what's bad...," Tashima added. "The biggest problem, however, remains governance...
"Selflessness is my motto... At this stage, I think my chances of winning are about 20% to 30%, but as the campaign progresses, I want to raise my confidence to 40% or 50%. I truly want to change FIFA."
Former Tottenham Hotspur defender Ramon Vega was the first candidate to publicly declare his intention to challenge fellow Swiss Infantino last month.