Vanek met with Wild head coach Mike Yeo on Sunday.
"Is it a deal-breaker if he loves everything about the team and they're shorter term than another team? I don't think it's to that extent," Vanek's agent, Steve Bartlett, told the Star-Tribune. "It's just one more of those boxes that you check when you're trying to make a decision."
TFP has learned that Vanek could sign a three-year contract with Minnesota, if he opts against signing elsewhere.
Vanek, 30, is being courted by several teams, but has narrowed down his list in the recent days.
In addition to Vanek and Iginla, who is looking for a two-year contract, the Wild has shown interest in center Paul Stastny, though he's unlikely to join Minnesota.