The centre-back enjoyed an excellent season and reports have suggested that Gunners boss Arsene Wenger, who is thought to be keen to reinforce his defence, is considering making an offer.
Cahill, though, has indicated he will not actively seek a transfer elsewhere before the start of the next campaign.
The 23-year-old, who is on standby for England's World Cup qualifiers in June, told the Bolton News: "I'm happy and settled in Bolton.
"Since I've been at the club everyone has been outstanding; the manager, staff, crowd and players.
"It's a great place to come and play your football. There's a great togetherness in the club between the lads."
Cahill is keen for Bolton to take a step forward next season, but admits the club could find it difficult to attract star players.
He added: "It (this season) has been an improvement and we want to improve again next year, and we can do that by bringing a couple of players in.
"The squad is quite small but hopefully this summer we can add to it and strengthen.
"We all want to push on but whether you can do that is a different matter. It's a hard thing going out there and trying to attract class players to come in.
"We've got a small squad and we've not used that many players so it would be nice to have a few more options available to us, but it's easier said than done."