The Heat expect to "work something out soon" with Spoelstra, the source said.
Spoelstra's current deal with the team ends after the 2016-17 season, but both sides had long planned to finalize a new deal before the start of free agency on Friday.
Spoelstra, 45, served as a Heat assistant from 1997 to 2008 before taking over for Pat Riley as head coach beginning in the 2008-09 season. With the Big Three of LeBron James, Dwyane Wade and Chris Bosh, the Spoelstra-coached Heat won NBA titles in 2012 and '13.
This past season, Miami finished 48-34, good for third place in the Eastern Conference. It lost to the Toronto Raptors in the East semifinals.
Spoelstra is a career 399-241 in the regular season and 70-43 in the playoffs. He is the longest-tenured coach in the Eastern Conference and is second to only San Antonio's Gregg Popovich in the NBA.
News of movement on an extension for Spoelstra comes just days before the start of free agency. The Heat have nine free agents, including Wade, Hassan Whiteside and Luol Deng, set to hit the market Friday at 12:01 a.m. ET.
In addition to likely locking up a long-term commitment with the Heat, Spoelstra is also set to wed fiancee Nikki Sapp later this summer after announcing their engagement nearly a year ago.
Information from ESPN's Ramona Shelburne and Michael Wallace was used in this report.