Former Cowboys quarterbacks Tony Romo and Troy Aikman, who both made the jump from the gridiron to the broadcast booth, chimed in on Witten's impending decision recently in an interview with WFAA 8.
The news on the second day of the draft could affect Dallas' plans just a week after Witten suggested he might play until he was 40 and meant to return this coming season.
ESPN's sources said Witten leaned heavily on Jones in coming to a conclusion.
"He has not made any decisions that are definite at this time", Jones said Friday, per Rob Phillips of the team's official site.
Witten, 36, played 15 seasons and was an 11-time Pro Bowler.
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Witten's 1,152 receptions rank fourth in National Football League history and second among all tight ends to ever play the game.
The Dallas Morning News cited two sources in reporting that the Monday Night Football offer from ESPN would pay Witten between $4 million and $4.5 million annually.
Witten finishes his HOF-caliber career with 1,152 catches, ranking 4th in National Football League history, trailing only Jerry Rice, Tony Gonzalez and Larry Fitzgerald.
The news broke right before the start of the 2018 NFL Draft last week, and Witten told the Cowboys he needed a few days, possibly through the weekend, to make a final decision.
The Cowboys now have four players on their roster at the tight end position - Geoff Swaim, Rico Gathers, Dalton Shultz and Blake Jarwin. He was added to the Pro Bowl as a first alternate. Without Witten, more of that responsibility will fall on Prescott, who is entering his third season.