With Friday's 5 p.m. ET deadline for signing Draft picks approaching, Heaney and third-rounder Avery Romero are the Marlins' only two selections from the first 10 rounds who remain unsigned.
The Marlins have not commented on the agreement.
According to reports, Heaney was asking for the $2.8 million signing bonus slotted for the No. 9 overall selection; the team offered $2.6 million. Per team policy, Heaney would have to pass a physical before he could sign a contract, and no such physical has taken place.
President David Samson offered little insight into the team's negotiations.
"I'll talk again [on Friday] at 5," Samson said. "We'll be here [on Friday] at 5. There's no reason to talk about it now."
Should the Marlins not sign Heaney, they would receive the No. 10 overall pick in the 2013 First-Year Player Draft.