Kelce has inflammation in his knee and the Chiefs will test it again Wednesday to determine his availability for the NFL's season opener Thursday night against the Detroit Lions, the source said.
"He's got some swelling going on," Jason Kelce said. "From what we know right now, his knee is fine. It's about getting that swelling down and [seeing] how bruised that bone is."
Chiefs coach Andy Reid had said Kelce suffered a hyperextended knee during Tuesday's practice.
"The next guy steps in and we roll," Reid said when asked how the game plan might change without Kelce. "That's what you do if [he doesn't play]."
Wide receiver Skyy Moore said he was running a route on the play when Kelce was injured.
"He was limping when I saw him, like, just walking off the field," said Moore, who added that Kelce left the practice field without any help. "It was a good sign to see him get up by himself and get off the field."
As for what the offense might look like against the Lions if Kelce can't play, Moore said, "It'll be a little bit different. ... Everybody will be able to fill in the gaps. Obviously, that's a Hall of Fame tight end, but we'll be able to do our job and pull across the finish line."
The Chiefs have two other tight ends on their active roster, Noah Gray and Blake Bell. Gray caught 28 passes with a touchdown last season. Bell missed most of the year with a hip flexor injury but has 60 catches with one touchdown in eight NFL seasons with five teams.
"He's one of the toughest, and we can't wait for him to get back out there," Bell said of Kelce. "We're just going to keep doing what we do, and the rest of the guys in the room will be ready to roll."
The Chiefs also have two tight ends on their practice squad, and one, Matt Bushman, was with the Chiefs in training camp. Bushman said he received a few snaps with the starting group after Kelce's injury, something that normally wouldn't happen if he wasn't going to play in the upcoming game.
Reid also said Tuesday that there has been "no progress" in talks with holdout defensive tackle Chris Jones, who is seeking a new contract.
"We're focused on the guys that are here, getting ready to play the Lions, and that's where I'm at. If you're not there, you're not there, that's the name of this game," Reid said.
Kelce, who has surpassed 1,000 receiving yards in seven consecutive seasons, has not missed a game to injury since his rookie season in 2013, when he underwent a microfracture procedure on his knee. The 33-year-old has missed only three games since 2014: twice resting in the final week of the season, in 2017 and 2020, and missing a Week 16 game in 2021 because of COVID-19.
The point spread on Thursday night's game moved after the news of Kelce's injury, with Kansas City dropping from -6.5 to -5 at Caesars Sportsbook.
ESPN's David Purdum contributed to this report.