Austin, a restricted free agent, was given a first- and third-round tender worth $3.168 million.
Dunn wouldn't comment if other teams have shown interest in giving Austin an offer sheet. The deadline for signing offer sheets by restricted free agents is April 15.
Asked again if he was hopeful to have a new contract in place by the start of the 2010 season, Dunn said, "sure."
Dunn and the Cowboys have held very preliminary discussions regarding a new contract.
"Nothing new. Nothing happening," said Cowboys vice president Stephen Jones regarding any new contracts.