The 26-year-old number eight suffered his latest injury in Bath's 40-26 defeat by Wasps on Christmas Eve.
Wales start their Six Nations campaign in Italy on Sunday, 5 February
"He is progressing well and back running," said McBryde. "It's a bit too early to say 'yay' or 'nay' for Italy."
Faletau was sidelined for over two months with damage to the same ligaments earlier this season.
McBryde added: "We have a good relationship with the Bath physios and it's going in the right way and progressing well - everything is going in the right direction.
"It has been well documented and everyone knows his strengths, he's world class."
Bath have an Anglo-Welsh Cup game against Gloucester on Friday night, but McBryde appeared to rule Faletau out of that fixture.
"Not this weekend, that would be rushing things," said McBryde.
"We want to see how things go this week and next week make that decision closer to the time.
"Ideally it would be great to give him some game time before the following week."
Faletau has played in only four games for Bath, having joined from Newport Gwent Dragons this season.
And the 2013 Lions Test player missed three of Wales' four autumn internationals in November 2016.
He played in the 27-13 win over South Africa on 26 November, creating a try for Justin Tipuric as Wales beat the Springboks for only the third time.
Meanwhile, Wales scrum-half Rhys Webb captained Ospreys in their Challenge Cup victory over Newcastle on Saturday, his first match since suffering an ankle injury against Australia last November.
Wales have the option of asking Webb to play for Ospreys in the Challenge Cup match against Bristol in Bridgend on Saturday.
Taulupe Faletau's recovery from a knee injury is "going well", but Wales forwards coach Robin McBryde says they do not know if he will be fit for the start of the Six Nations.