"I messed up, I spoke to the integrity unit about what happened but they didn't ask me about the TikTok videos, they just asked me about the pictures and I've already told them about that," Cleary told The Daily Telegraph in April.
"I wish I hadn't done the video, just got carried away in the moment. I was stupid. I messed up."
The NRL released a statement on Monday night revealing the duo were "untruthful" during the TikTok saga.
"The National Rugby League has issued Penrith player Nathan Cleary with a further amended breach notice," the statement read.
"The notice sets out additional matters to which Cleary has been asked to respond. The additional matters relate to his co-operation with the NRL Integrity Unit. The further amended notice proposes a fine of $30,000 and a two-match suspension, which would be served at the resumption of the NRL competition.
"Fellow Penrith player, Tyrone May, has also been issued with a breach notice relating to the same matter and his co-operation with the NRL's investigation. The notice proposes a $15,000 fine and a two-match suspension.
"The notices allege that the players were untruthful in relation to material matters and the proposed sanctions reflect the seriousness of those allegations."
Both players are able to respond before the sanctions are formally handed down. A successful appeal could overturn the two-match suspension.