Parent Telefonica explored a London listing for the mobile operator in 2016, after a merger with rival operator Three collapsed.
The mobile operator had been expected to list on the London Stock Exchange in this year following 4G and 5G spectrum auctions in April, but sources told the Press Association that those plans are now on hold.
The decision to put off its Initial Public offering comes at a time of market uncertainty and after a spate of underwhelming launches on to the stock market.
Accountancy giant EY has previously said that Brexit uncertainty is casting a "shadow" over the London IPO market.
O2's Spanish parent company Telefonica first said it would explore a London listing for its mobile operator in 2016, after a merger with rival operator Three collapsed amid competition concerns.