The Cavs did not accept Thompson's most recent offer of a three-year maximum contract that his side put on the table last week.
It now seems likely Thompson will miss the start of practice Tuesday, but the sides are not framing the situation as a holdout at this point. Thompson has until Thursday to accept the Cavs' one-year qualifying offer of $6.9 million that would enable him to become an unrestricted free agent next summer.
"We love Tristan Thompson and we want him to be part of our future," general manager David Griffin said Monday. "I think everything in our actions and our offer indicate that. ... We're excited about moving forward with him into the future in whatever form that may take.
"There's nothing lost by what Tristan is doing in this process. This is his right to do this. This system works for a reason."
Because Thompson is not under contract, he is not subject to being fined for missing media day or any practices.
By Thursday, Thompson must either agree to a new long-term contract, sign the qualifying offer or mutually agree with the Cavs to extend the qualifying offer deadline further and a holdout situation becomes legitimate.
There hasn't been much agreement on anything as talks yielded no progress over the weekend.
The Cavs have made several different offers over the summer, going as high as $16 million in an average annual salary for the versatile and athletic big man. Thompson has been resolute in getting a three-year, $53 million max contract or a five-year deal for $94 million.
With a market expected to be saturated with money next summer, Thompson's side made it clear he'd be willing to sign the qualifying offer and test the market again in 2016. But it appears both he and the Cavs may use all the of time before the Thursday deadline to try to find common ground.