However, Farnaby has revealed that he and King still managed to get their pawprints on the new movie and will be 'loitering around in the alleyways at the edges of that production'.
"Paul and I did tentatively write a story for Paddington 3, so we are involved. And I think Paul is involved at an executive level. We did have an idea for it," Farnaby told Yahoo.
The writer and comedian was promoting his work as the writer behind charming British comedy film The Phantom of the Open.
Farnaby added that the third Paddington film is moving forward and looks set to be "brilliant", with shooting due to take place later this year.
"They've got great writers and I think they've got a great director, so I think it will be brilliant, but we're slightly to one side for now," said Farnaby. A director for Paddington 3 has yet to be officially announced, and Studiocanal offered a 'no comment' on Farnaby's update.
Mark Burton (Paddington 2/Shaun The Sheep: Farmageddon), Jon Foster and James Lamont (Cuckoo/The Adventures of Paddington) are writing the script.
Watch: Paddington 3 set to begin filming in 2022
Farnaby took on a co-writer role for Paddington 2 after making a cameo appearance in the first film, which was also directed by King.
The duo had worked together frequently over the years, including on surreal TV series The Mighty Boosh and sort-of-spin-off film Bunny and the Bull.
Read more: Hugh Bonneville provides Paddington 3 update
But Farnaby said that after spending years working on movie adventures for Michael Bond's ursine hero, it was time to pass the baton to somebody else.
He added: "We love Paddington and we love [Heyday Films] and the people who make it.
"But it takes a long time to do those films. Paul did the first one himself, which took five years, and then [Paddington 2] was two and a half or three years.
"So we needed a break and to hand it over to someone else. But we are involved and loitering around in the alleyways at the edges of that production."
Read more: Hugh Grant's kids don't like Paddington 2
It'll certainly be tough to match the success of Paddington 2, which was a hit with audiences and spent time as the highest-rated movie of all time on review aggregator Rotten Tomatoes.
The Phantom of the Open sees Farnaby on writing duties once again, adapting the biography he co-wrote of notorious golf hoaxer Maurice Flitcroft.
Played in the movie by Mark Rylance, Flitcroft was an amateur golfer who duped his way into the qualifying round for the British Open — subsequently registering the worst score in the tournament's history.
He made several further attempts to enter the competition and became a tabloid sensation, as well as an embarrassment to the sport's powers that be.
Directed by actor-turned-filmmaker Craig Roberts, the movie premiered at last year's BFI London Film Festival and also stars Sally Hawkins and Rhys Ifans.
The Phantom of the Open is in cinemas now.
Watch: Trailer for The Phantom of the Open