Vannett (knee) is expected to miss 2-to-4 weeks, Jeremy Fowler of ESPN.com reports.
The blocking-oriented tight end injured his knee during Monday's preseason game against the Jaguars, while fellow tight end Adam Trautman hurt his ankle. The position already looked like a potential weakness for the Saints after they parted ways with Jared Cook and Josh Hill in the offseason, and a trade would make sense now that the top two guys on the depth chart are banged up. Vannett is an extreme long shot for fantasy value this year, but his absence could have some impact on playing time for the team's more receiving-oriented TEs (i.e. Trautman and Juwan Johnson).