Judy Murray said establishing the school of excellence in the capital was going to prove too expensive and plans for the facility have been scaled down.
Andy and Judy Murray met First Minister Alex Salmond during the tennis star's homecoming parade in Dunblane last month after his Grand Slam triumph.
The world No 3 and Mrs Murray discussed plans for the academy, with the preferred location for the academy being the former Dunfermline College of Physical Education in Cramond.
Andy Murray said he was prepared to help fund the new national tennis academy.
Plans had been drawn up for eight outside courts, eight inside courts and a cafe and gym.
The facilities were intended to boost outreach programmes, allowing children from deprived areas a chance to play the game.
Homes had been built on the Cramond plot, but 15 acres were reserved for sporting purposes as a condition of sale to the developers.
No figures for the original plans were available, but it had been hoped the centre would cost less than one-quarter of the £40 million it cost to construct the National Tennis Centre in Roehampton, south-west London.
Now Mrs Murray, coach of the UK women's Federation Cup team, has told how a smaller centre, estimated to cost £3m-£4m, is being considered closer to home.
She said she hoped similar centres could be set up across the country as the number of youngsters playing the game increases. Mrs Murray said: "We looked very, very closely and for a long time at a site in Edinburgh but it was going to prove to be too expensive for us.
"So we have really revised what it is we are looking for, and at the heart of it is this legacy not just of what Andy has achieved in tennis but the wonderful summer of sport we've had.
"That got me thinking that we need a smaller facility and a bigger outreach programme so that we can deliver our message further and wider.
"My preference would be for it to be in the Stirling area, which is obviously where we're from, and for us to be able to leave behind a facility and a very vibrant tennis community in our backyard would be absolutely wonderful.
"It would probably cost about £3m or £4m and we would invest in it for sure."
Mrs Murray said she expected the Lawn Tennis Association and the Scottish Government to also help fund the academy.
She added: "We are not setting it up as a money-making business; we want to share what we've experienced, share what we believe in and help tennis grow in Scotland.
"We don't need a huge facility to do that from. If we had six or eight of these dotted around Scotland as hubs of tennis activity we would be in a much stronger position in 10 years' time."
A Scottish Government spokesman said: "The Murrays are passionate about developing tennis in Scotland and the Scottish Government is equally ambitious to improve the participation of young Scots in the sport.
"We are continuing to explore opportunities with them and hope to make an announcement in the near future."
A Tennis Scotland spokesman said: "We will work closely with Judy and will play our part in doing what is best for tennis in Scotland."
Andy Murray trained at the Sánchez-Casal Tennis Academy in Barcelona and has told of the difficult decision to leave his home in Scotland for Spain at the age of just 15.
The Olympic gold medal winner shares his mother's zeal for attracting children to sport in general and tennis in particular.
He is said to be insistent that tennis should not be just for the privileged few and sees an outreach programme as central to the academy's purpose.
In a direct reaction to Murray's victory in the final of the US Open, and a golden Olympics, sporting bodies told MSPs that Scotland needed to secure a legacy from the summer of sporting success.
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