The crash between HMS Vanguard and French submarine Le Triomphant, which was also carrying nuclear warheads, is believed to have occurred on February 3 or 4.
Despite being equipped with sonar to detect other vessels, neither submarine apparently realised the other was in the same part of the ocean.
A senior Navy source told a newspaper the potential consequences of such a collision were "unthinkable".
He said: "It's very unlikely there would have been a nuclear explosion. But a radioactive leak was a possibility. Worse, we could have the crew and warheads. That would have been a national disaster."
A Ministry of Defence spokesman insisted nuclear security had not been breached. Inquiries are under way on both sides of the Channel.
A statement from the First Sea Lord, Admiral Sir Jonathan Band, said: "Two submerged SSBN, one French and the other UK, were conducting routine national patrols in the Atlantic Ocean.
"Recently, the two submarines came into contact at very low speed. Both submarines remained safe and no injuries occurred.
"We can confirm that the capability remained unaffected and there has been no compromise to nuclear safety. HMS Vanguard returned safely to Faslane under her own power on 14 February."