Kelemete, an exclusive-rights free agent, is expected to have an opportunity to compete for a starting job in training camp this summer.
The exclusive-rights tender would cost the Saints a one-year deal worth $585,000. According to Woodbery, New Orleans has Saints told Kelemete that they plan to exercise the extension.
Kelemete, 24, was taken in the fifth round of the 2012 NFL Draft by the Arizona Cardinals. However, he lasted just over a year with the team before he was placed on waivers at the start of the 2013 season.
The Saints later signed him to their practice squad and gave him a future/reserve contract close to a month ago.
In 2014, Kelemete was active for 10 games, but was limited to playing just six snaps.