"I've only spoken to him on the phone," Gillis told Team 1040 Radio on Thursday. "I'm going to go and have a visit with him in the next little bit.
"Roberto and I have a very good relationship, and we'll be able to talk about all of the issues, and I'll know more when I see him."
Luongo lost the No. 1 job to Corey Schneider during the 2012 Stanley Cup Playoffs, but the Canucks were unable to trade the 34-year-old and his expensive long-term contract. The Canucks instead traded Schneider to the New Jersey Devils at the 2013 NHL Draft last month.
Gillis said he was not worried about possible hard feelings from Luongo.
"He's always been a professional, and I'm sure he'll remain a professional and he'll act in the best interest of his hockey team and himself," Gillis said.
Canucks owner Francesco Aquilini reportedly met with Luongo in Florida last week. Gillis said his meeting with Luongo was not delayed by the goalie's participation in the World Series of Poker. Luongo was knocked out of the event Wednesday.
Luongo on Monday gave an interview to a Las Vegas radio station that was limited to questions about the poker tournament. According to the Vancouver Province, he was asked, "Aside from poker, what's new? What's up?"
Luongo responded, "Not much. Just enjoying the summer, working out and getting ready for another big season."