The Ducks declined to make qualifying offers Monday to five players, including forward Brandon Pirri.
Lindholm and Rakell are key components of the Ducks' roster, while Noesen is a valuable prospect.
The 22-year-old Lindholm has 96 points in three full seasons with Anaheim. Rakell broke through last season with 20 goals and 23 assists, ranking fourth on the team in scoring.
Anaheim acquired the speedy Pirri from Florida in February for a sixth-round pick, but an ankle injury and an upper-body injury limited him to nine games for the Ducks.