The meeting was described as "preliminary," according to a source, as Riley attempted to sell Deng on the benefits of joining the four-time defending Eastern Conference champions.
Sources told ESPN The Magazine's Chris Broussard that Deng will not take a salary significantly below his market value, believed to be above $10 million annually, merely to sign with the Heat.
Deng has several suitors, including Dallas, Atlanta, Chicago and the Los Angeles Lakers, but a source said Riley's pitch intrigued him.
The challenge facing the Heat is that Riley doesn't know exactly how much money he can offer Deng because LeBron James, Dwyane Wade and Chris Bosh, who opted out of their Miami contracts, have yet to sign contracts.
Deng has meetings with other teams scheduled for next week. It is not clear whether he will meet again with Miami.
ESPN's Josina Anderson contributed to this report.