'We're not all liars'
Throughout the protracted saga, both Blatter and Platini have insisted the payment was part of a legitimate oral contract.
Platini was hired by FIFA as a consultant from 1999 to 2002 and had apparently not received his full compensation.
The two men claimed the $2 million was authorized in 2011 as an honest effort to settle that account.
Judges at FIFA and CAS have so far found that argument unpersuasive.
Blatter has maintained his innocence as his four-decade FIFA career unraveled over the past 13 months.
"FIFA made the contract with Platini, and this was an oral contract," he said in Zurich.
"So far in the FIFA committees, in the ethics committee and in the appeal committee, they were saying, 'We don't believe that. But we are not all liars. I think there is a good chance that this panel will believe there was a contract."
Arguments at CAS are expected to last just one day, although a decision might take several weeks.
The hearing marks the latest legal battle in a series of intertwined scandals that began in May of last year when the US Justice Department unsealed a raft of corruption indictments against top FIFA officials, culminating in a Zurich raid that resulted in multiple arrests.