Linehan joined the Cowboys from the Detroit Lions last month in a major reshuffle of the staff, with Bill Callahan demoted to a running game role and head coach Jason Garrett surrendering all offensive duties.
"Linehan gives us a complete real change of our offense with our terminology. It's different. Although [Garrett and Linehan] have been together coaching, you can't see a lot of what we've been and what they did up in Detroit," Jones is quoted as saying by ESPN.
"He's got a track record of really zeroing in and building the offense around the talent, the specific talent and the qualities of the players."
The Cowboys finished last year with an 8-8 record, missing out on the playoffs for the fourth year in a row.