The former First Minister said the tennis player would be the “most popular Scottish knight since Sir William Wallace”.
Murray won a second Wimbledon title last month, after first lifting the trophy in 2013.
The Dunblane-born champion also won the US Open in 2012, an Olympic gold medal at the London 2012 games and steered Great Britain to victory in the Davis Cup last year.
Mr Salmond caused controversy when he unfurled a Saltire flag at Murray’s 2013 Wimbledon win, while some of the Centre Court crowd booed Mr Cameron at this year’s final.
Noting that Murray was not given a knighthood in 2013, Mr Salmond said: “I would say Andy Murray would be the most popular Scottish knight since Sir William Wallace. Winning Wimbledon should make it a slam dunk.
“David Cameron gets a resignation honours list so it’s a chance to right a wrong from his time as Prime Minister.
“If Cameron has got over the Saltire incident from 2013 and then getting booed by the All England Club this year, I think the decent thing would be to put Andy on his resignation honours list.”
The last Prime Minister to issue a resignation honours list was John Major, with Tony Blair and Gordon Brown choosing not to.
Mr Cameron’s list is expected to be published in the coming weeks.
Three cyclists have previously been similarly honoured: Sir Chris Hoy in 2009, Dame Sarah Storey and Sir Bradley Wiggins in 2013.