Frenchman Platini, who was re-elected for a third term as UEFA president earlier this year, is likely to decide within the next 10 days or so whether to run, the source added.
Platini was repeatedly promised support at meetings with confederation representatives held late into Sunday night at a luxury lakeside hotel in Zurich, the source said.
FIFA's executive committee was meeting on Monday to discuss reform plans and set a date between December and February for a vote to replace outgoing president Sepp Blatter.
Blatter was elected for a fifth term at the congress in May but announced on June 2 that he would step down as a corruption scandal engulfed FIFA. He himself has not been accused of any wrongdoing.
As well as UEFA, the continental confederations representing South America (Conmebol), North and Central America and the Caribbean (CONCACAF), and Asia (AFC) have all reportedly told Platini they would back his candidacy for FIFA president.
The other two confederations are Africa's CAF and Oceania's OFC.
Platini was once considered Blatter's protege and a natural successor to the 79-year-old Swiss. The two have become rivals in the last year, however, and Platini urged Blatter not to stand for a fifth term in May.
United States prosecutors threw FIFA into turmoil in May by indicting 14 sports marketing executives and soccer officials, including a number from soccer's governing body. Seven were arrested in a dawn raid on a luxury Zurich hotel just two days before the Congress at which Blatter was re-elected.
Each of FIFA's 209 member associations holds one vote in the presidential election.
Image: Michel Platini
Photograph: Harold Cunningham/Getty Images for UEFA
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