Voltar
The centre-back was a target for Dundee, who wanted to sign him on loan after he didn't play much at Parkhead last season.
However, he opted to remain with the Hoops, and has now started four games in a row.
Murray stated that his focus was always on Celtic, despite the speculation surrounding his future.
He said: "A lot of speculation was around Dundee at the time, but for me it was ultimately just to keep my head down.
"I don't really listen to that stuff.
"I think I always want to play here, that's my main focus.
"My main objective is to play at Celtic and be here for as long as I can do."
Murray also expressed his delight at playing with his friend, Colby Donovan, who has been a regular in the right-back position.
"We're right good pals, so it's good playing alongside him," said the 23-year-old. "We do a lot off the pitch together.
"Everyone's really close in the group. We all get on really well, so it's good to have a team full of mates."
Murray is also benefiting from the experience of seasoned players like Callum McGregor, Liam Scales, and Kieran Tierney.
"It's massive," said the academy graduate.
"They're all international players. They've made plenty of appearances for this club, so if I can take a wee bit off them, I'll be doing alright."