Everton ended their pursuit of the Portuguese after Watford made it clear their head coach was staying.
The Merseyside club offered Watford £15 million in compensation but were told no financial offer would be accepted, and are now in talks with former Crystal Palace and West Ham boss Sam Allardyce.
Silva signed a two-year contract when he joined in the summer, but refused to deny he was interested in a move to Goodison Park.
Asked by Standard Sport if supporters should have any concerns about Silva being distracted by the furore, Duxbury said: “Marco is an exceptional head coach and is fully focused on the job here. I don’t want to talk about the speculation that’s been going on. Our position on that is well documented.”
Standard Sport understands Duxbury wrote to Everton to warn that Watford would report the club to the Premier League if they continued to pursue Silva.