The 26-year-old Schneider was set to become a restricted free agent on Sunday.
"We have agreed in principle to a deal with Cory Schneider. More news in the next few days," Gillis posted on his official Twitter account.
Schneider took over in goal for Vancouver starter Roberto Luongo in this year's playoffs as the Canucks were upset in the first round by the Los Angeles Kings.
The Canucks have made it known this off-season that they are looking to trade Luongo and the remaining 10 years on his mammoth contract.
Schneider earned US$900,000 last year and is due for a hefty raise.
In 68 career games, the Marblehead, Mass., native has a 38-17-4 record with a 2.24 goals-against average and a .928 save percentage.