Security correspondent Frank Gardner said the BBC had been told "more than one concerning issue" had been uncovered regarding Mr Williamson during the leak inquiry and not just the Huawei conversation.
Gavin Williamson has hit back at the "haphazard way" the Huawei leak inquiry was carried out, complaining to friends he was only fired because of information he had personally volunteered to investigators working for Downing Street.
Theresa May hoped firing her defense secretary over a leak would put her latest government scandal to rest.
Telling Mr Williamson of his dismissal, Mrs May said she was "concerned" at the manner in which he had engaged with Sir Mark's inquiry.
The Prime Minister has appointed global development minister Penny Mordaunt to succeed Williamson as defence secretary.
Williamson was apparently the source for a Daily Telegraph front-page story stating that the National Security Council, made up of senior Cabinet ministers, had chose to allow Huawei to supply equipment for the edge - but not the core - of the UK's future 5G networks. He has expressed the hope that the Daily Telegraph journalist he spoke to - Steven Swinford - would "do the right thing" and reveal his side of their conversation.
The government continues to insist that there is no need to involve the police, no need for a criminal investigation, no need for a trial of Mr Williamson.
The PM has grown used to leaks from Cabinet meetings on Brexit, as ministers fight to get their version of events out first. Adding to the concerns is the contest to replace Ms.
"At this time, we're not carrying out an investigation", the statement pointed out.
The drama has not stopped there.
He also took a jab at the investigation into the leak, saying that "a thorough and formal inquiry would have vindicated [his] position".
The government has attempted to bring an end to the controversy.
"The prime minister has said she now considers that this matter has been closed and the cabinet secretary does not consider it necessary to refer it to the police, but we would of course cooperate fully should the police themselves consider that an investigation were necessary", he said.
Opposition MPs have said there should be an investigation into whether the Official Secrets Act had been breached.
Nevertheless, the government has faced a backlash.
"This seems to have been a kangaroo court reaching a decision in secret which we have no evidence to base any decision on".
As the government attempts to contain the spiralling controversy, a damage limitation effort is also under way to maintain strong relations with the USA, which has reiterated its stark warning.
Disclosure of official information relating to security and intelligence by a "Crown servant" - including government ministers - can be illegal.
Huawei denies that its equipment is vulnerable to state espionage.
"The UK has to balance its relationship and its broader global need for trade deals with countries including China but not only China, with its long-term, close security relationship with the United States". Mr Jones also claimed that Mr Williamson "knows where the bodies are buried" and would be "plotting" his next move.