The Prime Minister stressed honours were decided independently but added: "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 had "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."
However, Murray, who was made an OBE after winning Olympic gold and the US Open last summer, has questioned whether that would be appropriate.
Quizzed on the subject at a press conference on Monday morning, he said: "It's a nice thing to have or be offered. I think just because everyone's waited for such a long time for this, that's probably why it will be suggested but I don't know if it merits that.''
Bookmakers have responded to Mr Cameron's comments by slashing Murray's knighthood odds.