The deal could be wrapped by Sunday, the source said.
Fritz would succeed Dana Holgorsen, who was fired by Houston last week after five seasons and a 31-28 record. SMU beat Tulane 26-14 on Saturday in the American Athletic Conference championship game.
Fritz declined to confirm his intentions after the game and said, "No," when asked if he had an agreement already in place with Houston.
Over the past two seasons, Fritz has led Tulane to a 23-3 record, including a Cotton Bowl win over USC and No. 9 final ranking in the Associated Press poll in 2022.
The Houston Chronicle first reported Houston was targeting Fritz.
Information from The Associated Press was used in this report.