Saints veterans reported to camp Thursday, with the first practice scheduled for Friday.
Thomas, who is due to make $1.148 million in the final year of his rookie contract, is subject to a maximum fine of $40,000 per day for missing camp.
Thomas, 26, participated fully during the Saints' organized team activities and minicamp practices earlier this offseason, telling ESPN, "I'm a football player first; I like being at work."
But the first-team All-Pro has been unable to work out a long-term extension with the Saints despite negotiating for weeks, according to ESPN's Adam Schefter.
Saints coach Sean Payton and general manager Mickey Loomis said they weren't surprised that Thomas was absent Thursday. But Payton said he is "optimistic" the matter will be resolved fairly soon.
"I've been around too long to be surprised," Loomis said. "It's always a negotiation. It's a give and take. And then ultimately the urgency that you'd like to have happen in February, March, April or May gets dragged out into training camp. It's just the nature of the business."
Loomis said he never knows when a deal is "close" until he sees the player in the team offices ready to sign a document. But he said he does not feel like this is a situation where the two sides are far apart. He said he has been in touch every day with Thomas' side (he is represented by agent Andrew Kessler), and that the talks have been professional and not contentious.
Loomis also said he doesn't like the fact that Thomas isn't at training camp despite being under contract, but that he's not disappointed or mad at the wide receiver because he has that right. And the GM said negotiations will continue even though Thomas isn't on hand.
Payton said Thomas is the only Saints player who did not report to camp.
A source told ESPN's Dianna Russini last month that the Saints were comfortable making Thomas the NFL's highest-paid receiver -- a title currently held by Odell Beckham Jr., whose deal is worth $18 million to $19 million per year with $65 million in guarantees.
Thomas could be seeking a significant bump from that amount, considering fellow top receivers such as Julio Jones, Amari Cooper, A.J. Green and Tyreek Hill are also seeking new deals that should continue to raise the salary bar.
Loomis said Thursday that reporters would have to ask Thomas' side whether it's waiting for other receiver contracts to get done around the league. But he said the Saints aren't waiting.
"We're gonna do a deal that we feel works for us, regardless of what the other teams may or may not do," Loomis said.
The Saints have never paid a skill-position player more than $10 million per year, which was the size of tight end Jimmy Graham's extension before he was traded away in 2015. But Thomas, who was drafted in the second round out of Ohio State in 2016, has played a bigger role in New Orleans' offense than any skill-position player to come before him in the Payton-Drew Brees era.
Last season, Thomas set franchise records with 125 catches and 1,405 yards while catching nine touchdown passes. His astounding catch rate of 84.5% in 2018 was the highest of any NFL receiver since at least 2001, according to ESPN Stats & Information research.
Thomas' 321 career catches are the most in NFL history by a receiver in his first three seasons. Beckham ranks second with 288.
The Saints have about $12 million in salary-cap space after they signed All-Pro defensive end Cameron Jordan to a lucrative contract extension earlier this offseason. But they have some serious budgeting issues to consider in the near future.
Next year, Brees, backup quarterback Teddy Bridgewater and guard Andrus Peat are among the scheduled free agents. Then running back Alvin Kamara, guard Larry Warford and linebacker Demario Davis come due in 2021, followed by cornerback Marshon Lattimore and offensive tackles Terron Armstead and Ryan Ramczyk in 2022.
The Saints also have more than $26 million in "dead money" scheduled to count against their salary cap in 2020 because of the way they have structured Brees' contract.