Crawley say they have received no approach from Swindon for management duo Richie Barker and Steve Coppell.
Swindon are searching for a new manager to replace Paolo Di Canio following the Italian's departure from the County Ground last week.
Di Canio has since confirmed he has no intention of returning to the Robins, who are currently fourth in npower League One.
Reports have emerged claiming Swindon have turned their attention to Crawley boss Barker and director of football Coppell, who have guided the Red Devils to 14th in their first season in the third tier.
But a Crawley spokesman told Press Association Sport: "There is nothing in it. The club have had no approach, and no-one has been in contact with our CEO."