The approach was made in April and the individual also offered to provide "what appeared to be illegally obtained" information relating to the financial activities of FIFA president Sepp Blatter, his campaign added.
The individual was not identified, although the campaign said he was a third party, who was not part of FIFA nor connected to any national football association.
The matter was referred to Quest, a UK-based corporate intelligence firm, who were asked to contact the police and the offer was rejected. FIFA's ethics committee, however, was not informed.
"Our goal was not to create a campaign issue but to properly react to an approach made to us that appeared to involve criminal activity," Prince Ali's campaign said in a statement sent to Reuters.
"The campaign did not want to do anything that could jeopardise the police investigation
"Because the claims made by the individual strongly suggested criminal acts, Quest referred the matter to the proper law enforcement authorities.
"We did not engage the FIFA Ethics Committee because the individuals concerned were third parties who were not part of FIFA, nor were they National Association representatives."
Quest, headed for former London police commissioner John Stevens said in a previous statement that Prince Ali had engaged them in January to ensure "the highest levels of integrity and ethical standards throughout his campaign for the presidency of FIFA".
"The individual's claims to have obtained information illegally are now under police investigation," Quest said.
"Prince Ali's campaign has not received any offers involving questionable behaviour or potential illegalities from FIFA member associations or individuals claiming to act on their behalf."
Prince Ali is the only challenger to incumbent Blatter in Friday's election after Dutch FA president Michael van Praag and former Portugal forwards Luis Figo withdrew last week. Blatter is runaway favourite to secure a fifth mandate.
Each of FIFA's 209 member associations holds one vote at the election.