CLEVELAND, Ohio -- The deadline for the Cleveland Cavaliers and Boston Celtics to finalize their blockbuster trade -- provided the two Eastern Conference powers don't agree to extend -- is fast approaching.

By Thursday morning, the two sides will finally have to figure out whether they are going to move forward with the deal as currently constructed, if another sweetener has to be tossed in to appease the Cavs, who have seemingly pressed pause as they sift through Thomas' medicals, or if they let the deal fall apart.

Given how far along the two sides are and what the Cavs are getting in return for disgruntled point guard Kyrie Irving -- Thomas, Jae Crowder, Ante Zizic and Brooklyn's 2018 unprotected first round pick -- former Cavaliers General Manager David Griffin believes protege Koby Altman should proceed as planned, saying he would make the same deal if still running the front office.

"I think I would have," Griffin told NBA TV late Tuesday night. "I really think Koby Altman made a tremendous trade here, given the circumstances. When you're trying to win a championship, there is no in between. You're all the way with me, or you're all the way against me. And I think this was a situation where Kyrie made it clear he had a goal set that might not have jived with what Cleveland's was.

"They made a deal that, even in the absence of Isaiah Thomas, is a tremendous collection of assets and value Koby was able to get. At the same time, Boston made a trade to get a piece that really could be the key for them -- a 25-year old player in his prime who is an NBA champion, an Olympic champion and is really just starting to scratch the surface of who he can be."

The swap seemed done last week. The Cavs sent out a press release thanking Irving for six "impressive years" and talking about how the trade allows the Cavs to remain a title contender while also satisfying their desire to protect their future.

But nothing can be official until all parties involved pass their physicals. That's where the holdup has occurred.

Thomas, who originally injured his hip in March and the re-aggravated the injury during the Eastern Conference Finals, was examined by Cavaliers doctors on Friday and has stayed in contact with them since. He informed ESPN Tuesday night that he has made significant progress and is confident he will be the same player -- even if there is chatter about him missing the start of the regular season.

"I don't think (Thomas' injury) was a surprise necessarily," Griffin said. "I think when you go through these deals, you share all the information you have and you share all the images you have. If the most recent images from Isaiah were as far back as the playoffs, then when you get a new set of images now that's going to create the ability to compare and contrast, and see how things have improved.

"So I don't think it's a situation where anybody was caught off guard. I think it was just a case of getting perhaps more information. Obviously, Isaiah is in this league because he has heart and soul and a resolve that is almost unparalleled, and I believe him when he says he's gonna be back to 100 percent and I don't think anything that has been revealed to this point should make anyone think he won't."

Multiple sources told cleveland.com that as of Tuesday afternoon, Cleveland hasn't asked the Celtics for anything extra. ESPN is reporting that the two sides have begun to engage each other on a "solution."

Thomas' status for this season is important, as the Cavs will need a short-term fill-in for Irving and Thomas, the league's third-leading scorer last season, seemed to be a stellar fit.

He will be a free agent next summer, seeking a huge payday, which gives him plenty of reasons to not rush a return. All of it has to be taken into account by the Cavaliers.

But in the end, Griffin believes the Cavs and Celtics both have incentive to somehow get the agreed-upon trade to the finish line.

"I guess sometimes in these situations you think of it as mutually assured destruction," he said. "There's not a lot of upside to this deal coming undone, for either side. Because of that, I think it will end up going through as is. Hopefully, they'll be able to get Isaiah to a point where he's ready sooner than people think.

"One of the real blessings of this is Koby and his team don't need to be done (trading) at this point. They can continue to try to build the team. The value-to-production of Jae Crowder and his contract are incredible. As you move closer to the trade deadline, the assets they've acquired may be able to be put to work again in continuing to improve the team. I think they clearly wanted to get some sustainability so that lottery pick was really important because in the absence of LeBron (James) that's the piece that helps them rebuild rather quickly."

Cleveland.com's Joe Vardon contributed to this story.