The Prime Minister said honours were decided independently but "I can't think of anyone who deserves one more".
He said Murray's victory, which saw him become the first Briton to win the men's singles title for 77 years, "lifted the spirits of the whole country".
The Prime Minister, who watched the straight-sets victory from the Royal Box, said: "It was a fantastic day for Andy Murray, for British tennis and for Britain.
"I think he lifted the spirits of the whole country.
"We were wondering yesterday morning 'Do we dare to dream that this is possible?' and he proved absolutely that it was."
Asked about the possibility of Murray becoming Sir Andy, Mr Cameron, a keen tennis fan, added: "Honours are decided independently but, frankly, I can't think of anyone who deserves one more."