No. Before 2011 when Djokovic had a career like the one Murray has now nobody talked about a big 3, they talked about Fedal.
It wasn't untill Novak started dominating, reached N1, won multiple slams and defeated Federer and Nadal in multiple ocassions in the same year that people started talking about the BIG 3.
Murray needs a few more slams and some weeks at N1 (and a year end) for a TOP 4 to exist. The other 3 are clearly above him.
This is true. Still, it depends on how you look at it. In terms of being 'too hard for most opponents to beat' and being an (almost) equal opponent in most of their H2H matches, then yes, there is a big4.
If you look at it through achievements, then no. As BA said in the quoted post, nobody was talking about the 'big3' in 2009/2010 even tho Novak had 1 Slam + Slam final, bunch of Masters, WTF title, #2 career high ranking and many smaller titles... All of the Fedalovic (that's how you call it) had (shorter or longer) periods of absolute dominance and everybody knew that that one player was the best in the world. Murray was never best in the world, never the #1 favorite in any Slam...
Define what you mean by 'big4' and you'll have your answer.