The English League One club have distanced themselves from reports of a move for the clubless Australia international, who recently returned to the UK
Kewell has moved back to the United Kingdom to be with his wife and her sick mother and needs a new club after a season in the A-League with Melbourne Victory.
British media reported on Sunday that Swindon manager Paolo di Canio was keen to recruit Kewell, but Wray has ruled out any bid for the 33-year-old Australian.
"There is nothing at all in it, no association at all," Wray said according to the Wiltshire Gazette & Herald on Monday.
"I have seen the rumours but there is nothing in them, the first I saw about it was in the media."
While Australian media picked up the story on Monday, the chances of Kewell joining Swindon always looked slim.
Di Canio's recruitment for the 2012-13 season has focused on youth as he attempts to take Swindon from League One to the Championship.
The 44-year-old Italian has signed seven players since the end of last season with an average age of almost 27, meaning Kewell would represent a distinct divergence from di Canio's recruitment strategy.
Kewell has already been linked with a move to Blackburn Rovers and Middlesbrough in what is likely to be his first stint in England since he left Liverpool in 2008.