The UEFA president is standing in the election in February to succeed Sepp Blatter but is now under investigation from FIFA's ethics committee - as is Blatter himself. Reform campaigners say unless Platini can publicly clarify the details surrounding the payment he should withdraw from the election.
The Swiss attorney general's officers interviewed Platini as a witness on Friday after opening criminal proceedings against Blatter.
The timing of the 2million Swiss franc payment in February 2011 needs to be explained, say campaigners. At the time Blatter was facing a challenge to his presidency from Mohamed Bin Hammam and less than two months later UEFA declared its support for the incumbent president.
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Blatter is also being investigated by prosecutors over TV rights deals he signed off in 2005 with now disgraced former FIFA vice-president Jack Warner.
Damian Collins, the MP who founded campaign group New FIFA Now, said there are key questions that FIFA and Platini need to answer.
Collins said: "If Michel Platini is able to not able clarify matters relating to his contract with FIFA and why he received such a large payment in 2011 for work he had supposedly completed nine years before, he should withdraw from the forthcoming FIFA presidential election."
He added: "Was the £1.35million accrued in FIFA's accounts from 1999? If it wasn't it would be a breach of Sepp Blatter's duties and would suggest that there was not believed to be any outstanding payments due to Mr Platini.
"Will FIFA and Michel Platini publish his contract and all correspondence relating to this payment?
"Finally, when did Michel Platini first raise the issue of the money he was owed by FIFA?"
Platini is understood to be preparing to send a letter to UEFA's 54 member associations to clarify the circumstances surrounding the payment.
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