The Coronation Street actor is accused of using racist language and being sexist.
The show's bosses have already formally warned him about "offensive" language during chats with R&B singer Alexander O'Neal.
He was also called out over "unacceptable" sexually suggestive comments directed at female housemates.
The 71-year-old's son, Roger, apparently posted an apology on behalf of his son on Facebook.
He said he would like to apologise to anyone "offended by my dad's behaviour".
Separately, Ofcom has received two complaints about the use of an offensive word by Katie Hopkins and four complaints over the incident in which former Baywatch star Jeremy Jackson pulled open Chloe Goodman's dressing gown.
The actor has since been chucked out of the house, also for "wholly unacceptable" behaviour.
The broadcasting watchdog will assess the complaints before deciding whether to investigate.
Channel 5 has not said if it has received new complaints but said it will be making an announcement regarding Ken Morley.
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Ofcom tells Newsbeat it has received 233 complaints about Ken Morley's behaviour on Celebrity Big Brother.