Adrian Wojnarowski of ESPN reported the news, noting the Heat were "working on" the extension, even though their preference to preserve cap space for 2021 is a "challenge" with Gallinari set to become a free agent this coming offseason.
This comes after Wojnarowski reported there was an "elaborate" three-team deal involving the Heat, Thunder and Memphis Grizzlies potentially in place that would result in Gallinari and Andre Iguodala playing for the Heat.
Gallinari has been a key piece for a Thunder team in playoff position with the No. 6 seed in the West. He is averaging 19.1 points, 5.7 rebounds and 2.3 assists per game while shooting 44.2 percent from the field and 41 percent from three.
While his departure would hurt OKC's chances this year, the team looks to be playing for the future despite its unexpectedly positive start to the season. He would give the Heat another legit scorer in a balanced lineup that features six players averaging better than 12 points per game for the No. 4 seed in the East.
Gallinari's range should fit well alongside All-Stars Jimmy Butler and Bam Adebayo. And with Iguodala, the Heat would acquire a two-time All-Defensive selection and three-time champion who can help lock down opposing wings with Butler, even at 36 years old.
There are still contract details to work out with Gallinari, but the Heat are clearly trying to load up to compete with the East's best come playoff time.