Bryant said he might lobby to return punts in Sunday's game at Washington.
"I think I am this week," Bryant said after Friday's practice. "'Cause I'm feeling it."
This is the healthiest Bryant has felt all season since suffering a thigh contusion in the Week 1 loss to the New York Jets.
Bryant has returned just four punts for 27 yards this season; last season, he returned two punts for touchdowns.
He would also like to return kicks, but that job could go to Jones, who should make his return Sunday after a four-game absence from a left high-ankle sprain.
Jones hasn't returned kicks since 2009 but has a career 24.2 average.
There are also no guarantees the Cowboys let Bryant work on special teams. He suffered his injury on a punt return and the team has been very cautious in using him there.
"It's 50-50," Bryant said.
On the season, the Cowboys are ranked 28th in punt returns and 27th in kick returns.
Calvin Watkins covers the Cowboys for ESPNDallas.com.