Executive vice president said he hopes negotiations with Smith's agent, Joe Panos, start "sooner rather than later."
Last week the Cowboys exercised the fifth-year option on Smith's rookie contract, which will pay him $10.039 million in 2015.
"We want to sign him," Jones said. "I think he wants to be here, and we want to get a deal done with him."
Smith has missed only one game in his three seasons and was named to the Pro Bowl last season. He played right tackle as a rookie but moved to left tackle in 2012 and blossomed in 2013.
Smith does not turn 24 until December. He is only three weeks older than the Cowboys' 2014 first-round pick, Zack Martin. Signing a player to a second contract at such a young age is almost unheard of. Jason Witten was 24 when he signed his second contract -- a six-year extension -- in 2006.
"That's what you love about those young guys," Jones said.