Murray, along with golfer Colin Montgomerie, has outlined ambitious plans for the new centre, which would include 12 tennis courts and a nine-hole golf course, at the 18th-century Park Of Keir between Dunblane and Bridge of Allan.
However, the 270-acre site has previously been a controversial battleground between developers and local community groups.
Residents have previously resisted any plans to build housing in the area, which could effectively join the two towns together.
Auchterarder-based developer A&L King has revealed it also hopes to build houses on the ancestral land, once owned by the Stirlings of Keir.
The 270-acre park once formed part of the boyhood home of the late Sir David Stirling, the Second World War hero and founder of the SAS.
In 1990, plans for a £70 million housing, tourism and business park on the spot split the community and led, after three years of struggle by the Stop Park of Keir group, to a 35-day public inquiry before the plans were scrapped. Further development plans were thwarted in 2003, 2004 and 2008.
Murray, mother of current Wimbledon champion Andy, will attend two consultation events later this month aimed at persuading people to back the plans.
Murray said: "This is a once-in-a generation chance for us to create a fantastic community tennis and golf destination that is affordable and accessible to everyone. We really hope that as many people as possible take the opportunity to come along and see for themselves what the project is all about."
When the plans were announced, Park of Keir Friends secretary Ann Shaw, said: "This is a very controversial area. It is green belt land and if houses were built there it would join up two distinct communities.
"We're keen to keep them separate - everybody is. So our position has not changed. We object to housing on that site."
Mark Ruskell, Green councillor for Dunblane and Bridge of Allan, has indicated he will oppose a residential development, saying: "The outcome of the last public inquiry was crystal clear in rejecting any housing on the site."
Consultation events will be held at Dunblane Community Centre on October 12 and at the Allan Centre on October 26.