Tennis Scotland has promised to provide charity Easterhouse Phoenix Development with mini-tennis equipment while it explores the possibility of building permanent tennis courts in the area.
At the moment, the nearest tennis courts are in Mount Vernon - a three-mile journey.
The council has now agreed to work with the charity and Tennis Scotland to look at increasing participation in the sport.
Richard McShane, founder of Easterhouse Phoenix Development, contacted the chief executive of Tennis Scotland, David Marshall, after hearing him speak about the need for facilities in deprived areas.
After Andy Murray won Wimbledon earlier this summer, Richard was contacted by a radio station who asked him if there could be any future tennis stars training in Easterhouse.
He said: "I told them 'not right now, that would be impossible, we don't have any tennis facilities. How would we have a world star tennis player if we don't have any facilities?'"
Once the equipment arrives in the next few weeks, Richard will offer it to schools to give pupils the chance to try the sport.
Richard said: "If we get a tennis facility for the area it will be brilliant. It is a great first step forward with Scottish Tennis doing this and we will look at the viability of a tennis court for the future."
David Marshall, chief executive of Tennis Scotland, admitted there was a facilities gap in the north-east.
He said: "In the longer term it is an area we will work in conjunction with other partners to look at the viability of getting new tennis courts."