The Manchester mayor had applied to stand as a candidate for the upcoming parliamentary by-election in Gorton and Denton.
Greater Manchester MP Andrew Gwynne says he is stepping down due to "significant ill health".
Andrew Gwynne is investigated over "actions causing significant damage to the reputation of the House".
Vincent Ricci claims he spoke up about the controversial group but has now been suspended over it.
Ged Cooney claims he was suspended for raising concerns about the group to party bosses.
Ryan had been summoned to a meeting with his chief whip after the Mail on Sunday published the texts.
Gwynne apologises for the "badly misjudged" messages and is suspended as a Labour party member.
MPs have a heated exchange over the reported lockdown breaching drinks in Downing Street