"No one's came to me and asked me to rest," Elliott said Sunday as the Cowboys opened up preparation for Thursday's game against the New Orleans Saints.
If they do, Elliott said he would listen.
"I've just got to go with what they believe is best for the team," he said.
Elliott said he has been dealing with the injury since banging the knee in the team's Oct. 3 win against the Carolina Panthers.
A day after the Thanksgiving Day loss to the Las Vegas Raiders, coach Mike McCarthy expressed concern for Elliott's health after the running back had just 25 yards on nine carries. Elliott has not topped 51 yards in his past four games, the lowest output of his career.
"It's that time of year," McCarthy said. "Zeke's running style is ferocious. He gives a pounding and he takes some hits. We need to evaluate that and this week we'll see what the preparation looks like for him."
A source told ESPN the Cowboys will consider providing Elliott time off to heal, including the possibility of holding him out of Thursday's game. The source does not believe placing Elliott on injured reserve is a consideration at this time. That would require Elliott to miss at least three games.
The Cowboys have scaled back Elliott's snaps in the past four games to help manage the injury. He has played 164 of 280 offensive snaps (58.6%) after playing in 379 of 451 (84%) in the first seven games of the season.
Elliott has missed just one game in his career because of injury (last December vs. the San Francisco 49ers, because of a calf strain). He was held out of the season finales in 2016 and '18 because the Cowboys' playoff position was set, and he was suspended for six games in 2017.
"He's the ultimate competitor," right guard Zack Martin said. "We see it on a day-in, day-out basis and I think everyone is seeing it. He takes great pride in being there for his teammates and doing whatever he can in his power to help this team win. For me, he's one of the top competitors I've been around, and he's going to keep doing that."