The six-foot-two, 208-pound left-winger had 43 goals last season with Buffalo, becoming the first Sabres player to reach the 40-goal plateau since Miroslav Satan did it in 1998-99.
The Sabres have scheduled an afternoon news conference with managing partner Larry Quinn and general manager Darcy Regier at HSBC Arena in Buffalo, N.Y.
The source said Vanek would receive salaries of $10 million and $8 million in the first two years of the deal before making $6.4 million in each of the remaining five seasons.
Buffalo, which won the President's Trophy for compiling the most regular-season points in the NHL, has to choose whether to match the offer or receive compensation in the form of four first-round draft picks.
Vanek, 23, a native of Baden bei Wien, Austria, was selected fifth overall by Buffalo in the 2003 NHL entry draft.
In two full seasons with the Sabres, Vanek has registered 68 goals and 64 assists in 163 career games.
He has also accumulated eight goals and four assists in 26 career playoff games.
This has been a tough off-season for the Sabres, who've already lost forwards Chris Drury, Daniel Briere and Dainus Zubrus, all of whom were unrestricted free agents. Drury signed a $35.25-million, five-year deal with the New York Rangers, Briere signed a $52-million, eight-year contract with Philadelphia while the New Jersey Devils signed Zubrus to a $20.4-million, six-year deal.