Kyle, who served four tours in Iraq, is credited with the most confirmed kills of any sniper in U.S. military history.
The bill, from Republican Roger Williams of Cleburne, would authorize the president to award the Medal of Honor posthumously to Kyle for his acts of valor during Operation Iraqi Freedom.
Kyle's wife, Taya, responded to the Medal of Honor proposal by sending a statement to FOX 4, which says, "It is a tremendous honor for Chris. He would be humble and tell you there were other heroes who deserved it more than he did. He would also say that his fighting and his life were never about the medals.
I feel Chris is still serving. I consistently hear about how his life is impacting others in a positive way.
The Congressional Medal of Honor is a tremendous blessing and tribute to a life well lived. Chris will be in wonderful company with other Medal of Honor recipients, just as he was on the battlefield with all our veteran heroes.
I know this would leave him feeling grateful, humble, honored, probably speechless and full of love for the country he loves so much. Thank you to everyone who made this possible."
Tuesday night, an Erath County jury convicted Eddie Ray Routh of murdering Kyle and Kyle's friend, Chad Littlefield, at a shooting range.
Routh was sentenced to life in prison.