With Scotland's first match against France on Feb 5, Morrison's best hope is recovering towards the end of the campaign which finishes with a home match against Italy on March 19.
But Morrison is crossing his fingers that he will be back fit before the clash with the Azzurri as Andy Robinson's men look to build on the momentum they created during the Autumn Internationals.
"I like to think of myself as a quick healer," Morrison told BBC Scotland.
"I've done this on the other knee before and I was back before they predicted.
"I'm hoping it will be around six to eight weeks, which would give me a chance to play in some of the Six Nations.
"I've been playing well this season, so to have this is a bit of a setback, but I'll just do my best to get back on the pitch."