Nintendo asked Criterion Games to revive the F-Zero franchise back in 2011, hoping that the creators of the Burnout series would be able to bring the series back as a launch title for the Wii U console in late 2012.
Criterion's founder Alex Ward confirmed to Nintendo Life that conversations did take place between the developer and Nintendo of Europe. He also confirmed that the game eventually didn't happen due to time constraints, with Nintendo wanting a demo to show off at E3 while Criterion were hard at work on multi-platform racer Need For Speed: Most Wanted.
F-Zero is chief among the series that Nintendo's fans want to see return. Only Metroid is considered a more widely-desired IP. We've certainly seen what could be hints at a return – in the form of an F-Zero mini-game in Nintendo Land and tracks in Mario Kart 8 – but those could easily be in place of any new game rather than hints that something is in the works.
Criterion's last main Burnout game was 2008's Burnout Paradise. The studio has since made spin-off Burnout Crash, two Need For Speed titles, and have helped with Battlefield: Hardline.
At E3 2014 they showed off a new IP but didn't show up at EA's press conference at this year's trade show.
As it stands, the wait for a new F-Zero goes on. We live in hope.