Jon Machota of the Dallas Morning News passed along Jones' response to a question about Garrett's job status during an appearance on 105.3 The Fan.
"It's not even a thought for me," he said. "... I think we're in a good spot with Jason."
Jones gave Garrett a vote of confidence last month after the Seattle Seahawks eliminated the Cowboys from playoff contention in Week 16.
"Just so we're clear about it: I do understand frustration right after you lose a game that has such meaningfulness as this ballgame," Jones told reporters. "But I get to look at a lot of different things and have been around a lot of head coaches and coordinators, so I feel good about our head coach."
He added: "There's no qualms or no issues, if you're talking about any place else relative to anything to do with the coaching—within certain boundaries, but specifically at the top. We've just got to get it done better."
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Garrett has compiled a 67-53 record across eight years as Dallas' head coach. The team has only qualified for the playoffs twice during that span, though.
Although the Cowboys failed to reach the postseason with a 9-7 record this season, the 51-year-old Pennsylvania native is only one year removed from being named the league's Coach of the Year after leading the team to a 13-3 mark in 2016.
Wide receiver Terrance Williams said during locker cleanout he believes the blame lies with the players, not Garrett or offensive coordinator Scott Linehan.
"We just didn't get it done. It had nothing to do with Scott. It had nothing to do with Coach Garrett," he said, per Drew Davison of the Star-Telegram. "I've been in this system for five years and it did me well. We have guys who can stand here and say, 'We didn't get the job done.' Plain and simple as that. We just didn't get it done."
Garrett remains under contract through 2019.