Rutherford has had trade talks with other teams about Ruutu, who is slated for unrestricted free agency July 1, but met with the Finnish forward this week to gauge his thoughts on staying in Carolina.
Rutherford liked what he heard.
"So our priority now is to try and re-sign him," Rutherford told ESPN.com.
Rutherford hopes to have a resolution on the matter before the end of next week. If the two sides can't find agreement on a new deal, odds are Ruutu will be traded before the Feb. 27 trade deadline.
Ruutu has been with Carolina since the 2008-09 season. He has 17 goals and 11 assists this year for the Hurricanes, who are 20-25-10 entering Thursday.
Pierre LeBrun covers the NHL for ESPN.com.