Cowen, 22, was limited to just seven games with the Senators last season, as a result of undergoing surgery on his left hip. He tallied one goal and 10 penalty minutes, but picked up three assists and 21 penalty minutes in 10 playoff games with the Sens.
The native of Saskatoon, Sask., is believed to be looking for a long-term contract, though both sides have presented long-term and short-term deals.
The Sun claims he could be asking for a deal similar to the seven-year, $27 million deal fellow defenseman Travis Hamonic signed with the New York Islanders last month.
Senators assistant GM Tim Murray and Cowen's agent Rick Valette are expected to continue discussions this week.
Cowen was drafted ninth-overall by the Senators in the 2009 NHL Entry Draft.