The Mirror says the Championship club wanted to sign Jones this summer but the £250,000 deal collapsed.
Preston could revisit the prospect of signing Jones, 21, when the window reopens. A host of League One clubs are also interested if Jones fails to head to Deepdale.
Jones played 24 times for Swindon in the third tier last season, scoring two goals.
He has also spent loan spells with Blackpool, Accrington and Cheltenham.