And a deserted toilet block in a separate West End park could become a community base, offering a wide range of services.
The city council carried out a marketing exercise to find tenants for the former equestrian centre at Linn Park in the South Side and the former public toilets in Kelvingrove Park.
As a result, councillors will be asked to agree that the Linn Park building should re-open as an equestrian and activity centre, run by a social enterprise.
It would provide activities for young people from disadvantaged background and for disabled children, offer riding lessons, work experience and a cafe.
The former toilets in Kelvingrove Park would be converted to offer free use of mobility scooters, free cycle hire to all school aged children, family cycle hire, back to work training and volunteering, a cafe, community meeting place and offer a pram and buggy park.
Alistair Watson, the city council's executive spokesman for land and environmental services, said: "We have been looking at a number of vacant buildings in our parks for some time.
"Ultimately, we want them to play a positive role in, and enhance people's enjoyment of, our parks.
"If the executive committee approves the report then real social benefits could be delivered in these two parks.
"The proposal for Kelvingrove Park outlines potentially significant social and community benefits.
"These include providing mobility scooters, to open up the park to people who may not have the opportunity to enjoy it to its fullest due to mobility issues.
"The free cycle hire for school aged children would be hugely beneficial to young people in the area and could have real health benefits.
"Linn Park would also benefit in a very real sense if the equestrian centre is brought back in to use.
"By supporting access to riding for young people with disabilities or from disadvantaged backgrounds, a whole new range of opportunities will be opened up to our young people.
"On top of this, the proposal also offers important training and work experience opportunities to young people."