Tanev, 24, has spent all four of his NHL seasons with the Canucks, who signed the Toronto native as an undrafted free agent in 2010. He set career highs last season with six goals, 11 assists, 17 points and a plus-12 rating in 64 games.
"He had a good season last year," general manager Jim Benning told the Vancouver Province. "He had a couple of injuries along the way, but he kind of took the next step. He's still a young player.
"We wanted to see another full season, another body of work this next season. ... If he has another good season, then we'll try to lock him up long-term."
In 156 NHL games, Tanev has eight goals, 27 points and a plus-26 rating. He has no points and nine shots on goal in 10 Stanley Cup Playoff games.
The Canucks announced Saturday they signed defenseman Peter Andersson; terms were not disclosed.
Vancouver's fifth-round pick (No. 143) in the 2009 NHL Draft, the Swede scored two goals and 13 points in 58 games last season with the Canucks' American Hockey League affiliate in Utica.
Andersson, 23, has spent the past two seasons in the AHL, where he has three goals and 21 points in 100 games.