An announcement on proposals for a tennis academy as well as nationwide improvements to facilities is expected in the near future, the First Minister has said.
Alex Salmond discussed the idea for an academy with Andy Murray during his homecoming celebrations at the weekend.
Murray and his tennis coach mother Judy argued that such an academy will help nurture young talent.
Speaking at First Minister's Questions, Mr Salmond told MSPs: "I was delighted to meet both Andy and Judy Murray last Sunday. It's clear both are passionate about developing tennis in Scotland to ensure that youngsters have greater access to facilities and coaching.
"We had a positive discussion about their idea for a tennis academy as well as improving existing facilities and indeed the overall interest in tennis, all of which is certainly in line with the Scottish Government's ambition to increase 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 that regard in the near future."
Murray, 25, was given a hero's welcome by thousands of people in a triumphant return to his hometown of Dunblane, near Stirling, at the weekend.
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.