Roger Federer and Rafael Nadal have both achieved the feat during their careers and the American says there is nothing stopping the Scot from doing the same.
Sock grabbed the eighth and final qualifying spot for the ATP World Tour Finals, which begin at the O2 on Sunday, but Murray is unable to defend his title because of a hip injury which has ruled him out for much of the second half of the year.
In his absence, Nadal and Federer, who missed out in London last year through injury, are the tournament favourites.
Sock told Standard Sport: “I think if Roger and Rafa can bounce back in the way they both have done this season, with the injuries they had, then Andy certainly can.
“I’m sure he’ll have many more times playing at the O2 and I see no reason why he can’t be going for Grand Slam wins next season.”
Murray’s absence is a big loss to tournament bosses, who can still lean heavily on the draw of both Federer and Nadal, who appears to have won his own pre-tournament fitness battle.
Sock added: “Obviously for the home fans, Andy’s a big loss, plus he’s one of the good guys.
“It was great to see him play in his exhibition match against Roger the other day, so I’m sure he’ll be back soon.”
A week ago, 25-year-old Sock was no more than an outside bet to make it to London and had no idea it was mathematically possible until someone told him during the Paris Masters that, if he won, he could make it.
He duly won his first Masters title to book his slot, and despite an opening match against pre-tournament favourite Federer — a player he has never beaten before — he believes he can continue his winning streak.
“Much like with Andy, Roger and I are friends off the court but, on it, it’s a battle,” said Sock. “I’ve not beaten him but I can take a lot of experience from those encounters and, after the biggest title of my career, I’m confident.
“As the last guy into the tournament, I think I can play freely. I’ve got nothing to lose.”