The 46-year-old is one of the candidates the Premier League new boys have targeted to replace Steve Bruce.
Coleman guided his country to the Euro 2016 semi-finals a month after signing a new two-year contract with Wales.
The FAW says everybody at the association is "fully focused" on the 2018 World Cup qualifying campaign.
Bruce resigned in July after a breakdown in his relationship with Hull vice-chairman Ehab Allam.
Roberto Martinez, sacked by Everton in May, and former Unites States coach Bob Bradley have also been linked with the vacancy.
Bruce, 55, joined the Tigers in 2012 and led them to promotion to the Premier League twice and also an FA Cup final appearance in 2014, losing to Arsenal.