The 57-year-old Australian was installed as the early favourite with the bookmakers after Graham Potter departed the Seagulls for Chelsea last week and, according to recent reports, remains a serious contender for the role.
Premier League clubs in England are understood to be taking note of Postecoglou's achievements at Celtic - winning the Premiership title and League Cup in his first season in charge - as well as his attacking brand of football.
But quizzed on the links to Brighton, who are currently fourth in the English top flight, Postecoglou insisted his sole focus was on Celtic, who face Shakhtar Donetsk in a Champions League group stage fixture in Warsaw on Wednesday.
“It’s not really relevant in my world or in my space," he said. "I have done that my whole career, I have just focused on being as successful as I can for the club I represent. If I do that, everything else takes care of itself because things change pretty quickly in football.
“If I’m not successful here, it won’t be other options that open up for me, it’ll be this one that closes.”
Postecoglou took charge of Celtic 14 months ago and asked if he felt it was still early days in his project, he added: “It is what it is.
"We’ve tried to sort of build the team as quickly as we possibly can. We did that last year knowing that we needed to bring success to the football club. We are in the Champions League now, so our role now is to be the best we can be in that and try to make an impact this year.
“Where that takes us, or how far that takes us, we’ll see at the end. I have always been mindful of making sure that every opportunity we get we try to grab. Whether it’s come too early or come at the right time, we do know that Champions League football is here for us and we want to take that opportunity.”