ESPN's Adam Schefter reported Monday that Thomas is "more likely than not" going to sign with the Texans this week, which led Jones to get asked during his weekly radio interview on 105.3 The Fan in Dallas why the team hasn't at least brought the seven-time Pro Bowl selection for a workout.
Jones explained he does see a need for improvement in the secondary but said signing a free agent may come with "demands" the team isn't willing to meet:
He added: "You can change personnel. But you might change the future structure of the roster. So that's a high price to pay."
Jones was previously asked about Thomas, along with fellow free agents Delanie Walker and Clay Matthews, following the team's Week 1 loss to the Los Angeles Rams, and replied that the team planned to address any lineup weaknesses "from within."
Now, with the Cowboys sitting at 1-2 following Sunday's loss to the Seattle Seahawks and the team's defense ranked 28th in passing yards allowed (277 per game), the topic was raised again. It doesn't sound like they'll make a last-ditch effort to keep Thomas away from the Texans, though.
The 31-year-old safety owns a strong track record. In addition to the Pro Bowl appearances, he's been named All-Pro five times (three on the first team and two on the second) and helped the Seattle Seahawks win Super Bowl XLVIII in 2014 as part of the Legion of Boom secondary.
Thomas recorded 49 total tackles, four passes defended, two interceptions, two sacks and one forced fumble in 15 games for the Ravens last season. It was his only year with the franchise before getting released in August after a training camp altercation with teammate Chuck Clark.
If the Texans signing proceeds as expected, he'll look to upgrade a unit that ranks 23rd in total defense (387.7 YPG) and 29th in scoring defense (31.7 PPG).
Meanwhile, Cowboys safety Darian Thompson has struggled with a lackluster 50.4 grade from Pro Football Focus through three starts in 2020.
Donovan Wilson and Reggie Robinson II are the team's internal reserve options at the position. Veteran cornerback Brandon Carr could also shift to safety to start alongside Xavier Woods.
Dallas is back in action Sunday when it welcomes the Cleveland Browns (2-1) to AT&T Stadium. It's the start of a three-game homestand for the Cowboys that also includes matchups with the New York Giants and Arizona Cardinals.