The Cowboys have held preliminary talks with the running back's agent, Drew Rosenhaus, according to multiple sources, and are offering a financial package in the $30 million range.
Barber wants a package between $40 million and $60 million.
Barber's asking price is comparable to deals given to Kansas City running back Larry Johnson (five years, $43.2 million), Washington's Clinton Portis (eight years, $50.5 million) and San Diego's LaDainian Tomlinson (six years, $60 million).
The Cowboys, according to the sources, believe the deal that free agent running back Michael Turner signed with Atlanta in March (six years, $34.5 million with $15 million in guarantees) is close to what Barber is worth.
Dallas is also willing to give Barber a contract close to what Baltimore gave Willis McGahee last year, a seven-year deal worth as much as $40.12 million, if the last two years of it are picked up.