"Alain and I have been meeting the last couple of days and we have a lot of things to discuss over the last couple of years about where we're headed, how we work together and how we view the world of hockey," said Gillis.
"That isn't something that happens in an instant. It takes a little time and often it takes getting into the clear light of day.
"I believe you just take your time and look at it clearly and thoughtfully and you'll get to the right conclusion. I know sometimes it doesn't happen on the schedule that people want or they want to interpret something into it, but that's just the way I do things."
Vigneault has one-year remaining on his current deal and has expressed the desire to return behind the Canucks' bench, while Gillis has also stated that he wanted his coach to be back.
"You have to have agreement and we're going to work together toward creating an agreement," Gillis explained last week.
Meanwhile, Gillis was much quieter when questions arose on the potential trade of goaltender Roberto Luongo, who is expected to lose his starting job to Cory Schneider next season.
The 33-year-old goalie, who has 10 years and roughly $47 million remaining on his contract, is likely to waive his no-trade clause, though Gillis did not encourage people to assume that a trade will definitely occur.
"I don't think you can assume anyone in any situation in this league will be moved," Gillis said.
"I think trades are very difficult to make. You have to work really hard at making a transaction and you have to do it for a lot of different reasons that often aren’t completely apparent to everybody analyzing it.
"We'll see how things go and progress for the next few weeks up to the draft."