Andy Murray has discussed his idea for a tennis academy with the First Minister during his homecoming celebration.
Alex Salmond said he had a positive discussion with Murray and his mother Judy about the idea to nurture young Scottish talent. The Scottish Government will explore the suggestion with the Murrays over the next couple of months, Mr Salmond said.
Murray, 25, was given a hero's welcome by thousands of people in a triumphant return to his hometown of Dunblane, near Stirling.
He celebrated a golden summer of success with locals just days into his return to the UK after beating Novak Djokovic to win the US Open. That victory came just weeks after he beat Roger Federer to take the Olympic men's title at London 2012.
"Scotland is very, very lucky to have Andy Murray whose legendary status is now secured for all time, and his triumphs at both the Olympics and at the US Open will act as a spur for future generations of Scots to emulate his success," he said.
"Both Andy and Judy are passionate about developing tennis in Scotland to ensure that youngsters have a greater access to the facilities and coaching that they need to make the most of their talent and potential.
"We had a positive discussion yesterday about their idea for a tennis academy which is certainly in line with the Scottish Government's ambition to improve young Scots participation in sport. We'll be exploring this with the Murrays and their team over the next two months and we hope to make an announcement in this regard in the near future."
The First Minister presented Murray with his official Royal Mail stamp for his medal success at the London Olympics where the Scot also won silver in the mixed doubles.
Murray did not attend Friday's official victory parade for Scotland's Olympians and Paralympians in Glasgow, having been advised to take a couple of days of complete rest at home after playing continuously for four months.