The Murdochs is a one-off drama set in the future, as Rupert Murdoch's family struggle to decide who should take over his media empire when he dies.
The script was rejected by Channel 4's former director of TV Kevin Lygo two years ago because it was too "media-centric", but it was rumoured that it had been revived following the News of the World phone hacking scandal.
The broadcaster's head of drama Camilla Campbell, who originally brought the idea to Lygo, is said to have been a fan of the script and recently told The Guardian that it was back in "active development".
"For me it never really went away, but with the stories about hacking I think the time could be right to make this," Campbell added.
However, speaking on Twitter, Armstrong has dismissed the claim. He said: "No - story of going into production incorrect sadly (sic)."
It was recently announced that Armstrong had signed up to write an episode of Charlie Brooker's new Channel 4 drama Black Mirror.