NFL Network's Jane Slater originally reported that the Saints are pursuing the Stanford head coach, followed by other outlets such as NBC Sports, but now other reporters are claiming that isn't happening - yet.
Nick Underhill of NewOrleans.Football was the first to report the opposite.
Saints beat reporter Matthew Paras then backed up Underhill's report.
The Saints fired former head coach Dennis Allen after Week 9 this season before appointing Darren Rizzi as the interim head coach. New Orleans went 3-5 under Rizzi before finishing the season with a 5-12 record.
However, Kansas City Chiefs offensive coordinator Matt Nagy is expected to receive interest from the Saints sometime after the NFL playoffs wrap up. The Chiefs are currently on a bye week after clinching the number one seed in the AFC and won't play until next weekend.
Shaw has been the coach of Stanford since 2011, is a four-time Pac-12 Coach of the Year Award recipient, and is the winningest coach in the program's history with a 96-54 record.