Former organiser The British Heart Foundation announced last week it was pulling out due to the Â£40,000 event no longer being viable.
However the council says it is "pulling out the stops" to ensure the fundraiser goes ahead as planned on 11 October.
The Save the Children charity has also announced it could "take up the baton", but only with financial support.
The council was working to reduce the cost through options such as changing the route or moving it to a completely different venue, such as Lydiard Park.
Last year, the race attracted more than 1,500 runners.
Swindon's half marathon could still be saved for the long-term by reducing its cost, the borough council has said.