The Russian hunter-killer allegedly struck a sonar line towed by HMS Northumberland, The Sun reported.
It would be the first collision between the Royal Navy and Russian ships since the Cold War, which ended in 1989.
The British warship was in search of the Russian submarine, about 200 miles north of Scotland.
In order to listen to the sounds of the submarine, the British ship took out its towed sonar, which is a cable covered with hydrophones.
However, the crew were reportedly forced to abandon their mission and return to port for repairs.
Former Commander Tom Sharpe said: “The question is whether this was a deliberate act or an accident.
“Detecting ships and submarines is not an exact science. It could have been a tight pass gone bad.
A Navy source reportedly said they believed it was a “random million-for-one event.”
“The crew of the submarine would have screwed each other,” he said.
“They would have heard a very sudden and unexpected noise like a fork being dragged over a cheese grater.”