Harris, who supplanted Max Hannemann as Lutui's agent two weeks ago, said he met with Cardinals general manager Rod Graves and others within the organization Monday.
Harris said Lutui wants a long-term deal. Lutui would have been an unrestricted free agent under the old salary-cap rules, which required four years of service. The threshold is six years in the uncapped 2010 season.
"Hopefully, things go well this season for him personally and the organization, and we'll evaluate what his feelings are, if he sees himself being a Cardinal in the future or if he sees himself hitting the market," Harris said.
Lutui's job as the Cardinals' starting right guard could be in jeopardy because the team recently signed free-agent guard Alan Faneca, who has a history with Ken Whisenhunt, the Cardinals' head coach, and Russ Grimm, the assistant head coach and offensive line coach, from their days on the Pittsburgh Steelers' staff. Starting left guard Reggie Wells also will return.