But Murray, who claimed his second Wimbledon crown with a straight sets win over Milos Raonic yesterday, may still travel to the quarter-final match in Belgrade to support Leon Smith's team as they start their title defence.
"It's possible", Murray told the BBC.
What about world number one? The last 18 months he's been unbelievable, he's hardly lost any matches at all so I know if I want to get there I'm going to have to try to win more matches against him. Over and over, Murray managed to get the ball back, even one that came in at 147 miles per hour.
Murray was back at the All England Club on Monday morning for another round of media interviews looking somewhat bleary eyed.
Serbian world number one Novak Djokovic, who suffered a shock defeat to Sam Querrey in the Wimbledon third round, will not be taking part in the contest, saying he was not feeling "100 percent". But after Djokovic's loss in the third round, and Murray's third Grand Slam trophy, the margin is 15,040 to 10,195.
"He was telling everyone it was allergies, that he had hayfever", Murray told a press conference.
"I believe I definitely have that ability within myself", he said.
"I spoke to Leon last night at the champions' dinner briefly". Murray won the tournament in 2012 and were he to win it again, it would mean he and Djokovic would have split the four majors in 2016.
With the victory, Murray has become the first Briton to win multiple Wimbledon singles titles since Fred Perry in 1935.
"Rio is obviously a big goal of mine and I hope I can perform well there".
After Sunday's victory, Murray's mother, former British Fed Cup captain Judy, referred to that old phenomenon as, "The constant, 'When are you going to win Wimbledon?". Celebrating such an epic victory was clearly new to him (just like winning Grand Slam finals was at the time).
"I feel a responsibility. I'll give it my best shot to do that".
But for Wimbledon champion Andy Murray, daughter Sophia proved to be the inspiration necessary to take him to the next level. I trust in what he says, mainly because of the results we had the last time we worked together. "I stepped up in a semifinal that twice I struggled in in the past, I came back from two sets to love down which is a first time for me, I showed guts, I showed vigour and I have to carry that through to the next events". I think it's going in a good direction right now, there's a few players doing well.