"I have not ruled out the possibility of him being a part of the Cowboys at all," Jones told reporters Saturday at the NFL Scouting Combine in Indianapolis.
Jones also said there is "nothing factual in any way" in regards to trade rumors involving Romo as part of a three-team trade.
"Haven't had a discussion with anyone," Jones said.
On Friday, NFL Network's Ian Rapoport reported that the San Francisco 49ers and Washington Redskins have already discussed a possible deal involving quarterback Kirk Cousins and may try to include Romo as part of the trade.
Jones told the Dallas Morning News that he had only one "real good, extended visit" with Romo since the 2016 season ended.
The Cowboys will not meet with Romo's agents at the Scouting Combine, but they expect a decision on the quarterback soon.
"I would say it's going to come," vice president Stephen Jones said earlier this week. "I think Jerry's going to be due to meet with him sooner than later, but I wouldn't say there's a definitive meeting as of yet."
The Cowboys could release Romo as early as March 9, the start of free agency, which seems more likely than a trade.
Romo, who turns 37 in April, holds many of the team's passing records with 34,183 yards and 248 touchdowns. But he hasn't played a full season since 2012, including missing 21 games with injuries the past two seasons.
Romo fractured his back during the preseason, losing his job to rookie sensation Dak Prescott while rehabbing. Romo's 2017 cap number of $24.7 million stands as the highest among any quarterback for next season.