Players report to camp Friday in San Antonio, and the Cowboys will hold their first practices Saturday. Cowboys officials do not comment on current contract negotiations.
Bryant was the 24th overall pick of the draft and the second wide receiver taken. With the Cowboys starting camp early, it's difficult to determine the going rate for draft picks in the low 20s.
Michael Crabtree was the second receiver taken in 2009 -- with the No. 10 pick by the San Francisco 49ers -- and he signed a six-year deal for $32 million after a holdout that lasted into October. That deal, worth about $17 million in guaranteed money, could increase to $40 million if certain incentives are met.
Bryant is represented by agent Eugene Parker, who also represents Crabtree.
Cowboys vice president Stephen Jones recently said it shouldn't be difficult to sign players -- especially Bryant, because the team has a good relationship with Parker, whose clients include Felix Jones and Anthony Spencer. Mike Jenkins' contract also was handled by Parker.