Vanek, who also will become an unrestricted free agent Tuesday, met with the Wild on Sunday night, according the newspaper.
Iginla, who turns 37 Tuesday, scored 30 goals and 61 points with the Boston Bruins last season. His five goals led the Bruins in the Stanley Cup Playoffs and his seven points were ranked third before Boston was eliminated by the Montreal Canadiens in seven games of the Eastern Conference Second Round.
The Bruins have expressed an interest in re-signing Iginla but may not be able to fit him in under the NHL salary cap of $69 million.
Vanek, who lives in Minnesota during the offseason, had 27 goals and 68 points last season for the Buffalo Sabres, New York Islanders and Canadiens. Vanek finished the postseason with five goals and 10 points in 17 games and was demoted to the fourth line in Montreal's six-game series loss to New York Rangers in the Eastern Conference Final.