It is thought to be the first collision between Royal Navy and Russian vessels since the Cold War, which ended in 1989.
The British warship was in search for the Russian sub, roughly 200 miles north of Scotland.
In order to listen for sounds from sub, the UK ship let out its towed array sonar, which is a cable covered in hydrophones.
However, the crew were believed to have been forced to abort their mission and return to port for repairs.
Speaking about the damaged cable, a source told the publication: “It was badly chewed up and unusable.”
Former frigate captain Commander Tom Sharpe said: “The question is was it deliberate or was it an accident.
“Ship and submarine detection is not an exact science. It could have been a close pass gone wrong.”
A Navy source reportedly said they believed it was a ‘million-to-one chance event’.
“The crew of the submarine would have sh*t themselves,” he said.
“They would have heard a very sudden and unexpected noise like a fork being dragged over a cheese grater.”
Foreign Secretary Liz Truss told MPs: “Any Russian military incursion would be a massive strategic mistake.
“Russia is the aggressor here – we urge them to end their malign activity and stick to what they have agreed.
“The only way forward is for Russia to de-escalate and pursue a path of diplomacy.
“The free world must rise to meet this moment.”
A Ministry of Defence spokesman said: “In late 2020 a Russian submarine being tracked by HMS Northumberland came into contact with her towed array sonar.
“The Royal Navy regularly tracks foreign ships and submarines in order to ensure the defence of the United Kingdom.”