The local Swindon evening paper reports that the player will become the first signing of the summer at the County Ground, two years after signing for the Swans from Yeovil Town.
Amankwaah was very much a passenger last season aboard the Swansea train as they secured the League One title – he made just four appearances with none of them in the league and has not featured for the first team since the 1-1 draw with Havant at the Liberty back in January – an appearance that now looks set to be his last at the club.
It was different the season before as he made 29 appearances – 8 of them under Roberto Martinez – in the league following his relatively big money move (£250,000) from Yeovil.
Amankwaah started his career at Bristol City before loan spells at Torquay, Cheltenham and Yeovil before the latter made his move permanent in 2005.
Neither Swindon or Swansea have confirmed the move for the defender although Maurice Malpas – the Swindon manager – told the Evening Advertiser
"Things have been quite slow this summer but we are working hard behind the scenes to make things happen."
No fee has been mentioned in the reports and there has also been speculation of a move to Hereford although Swindon appear to be at the front of the queue.