The 30-year-old centre-back has reportedly been interesting Crystal Palace and Everton over the summer but the Wales captain is staying put.
Williams signed a new four-year deal last summer but has continually been linked with a move away from the Liberty Stadium and Monk issued a ‘hands-off’ warning to rival clubs in March.
Monk, who on Saturday stated that striker Bafetimbi Gomis was also not for sale, believes the coming season is a huge one for Williams with qualification for Euro 2016 up for grabs with Wales.
“Ash will be here, he’ll be here with Swansea,” Monk told TalkSport.
“I’ve got a good relationship with him, he’s our captain and obviously I played with him for many years as well.
“For the past six or seven years he’s been linked with a team in the summer, and whether that’s actual interest or driven by the papers and agents, I don’t know.
“But Ash is very committed to the club, he’s our captain and he’s captain of Wales as well, it’s a big year for him with qualification coming up with his country.
“I don’t think he’ll want to do anything that unsettles him, I think he’ll want to give himself the best chance to qualify with Wales and have a good season with Swansea as well.
“I know he’ looking forward to it and is fully focussed on the season ahead with Swansea.”