However, there's optimism that a deal for the left-back will eventually be reached, Ornstein adds.
It's understood that Arsenal are confident in their ability to sign Tierney to new terms should an agreement be reached between the two clubs.
Celtic are hoping to fetch a £25-million fee for the promising 22-year-old, the Daily Record's Michael Gannon reports.
The Gunners are searching for answers at left-back, as Sead Kolasinac has failed to impress manager Unai Emery.
Celtic manager Neil Lennon admitted the Scottish champions are bracing themselves for offers from clubs interested in Tierney, as well as midfielder Olivier Ntcham, this summer.
"I would expect bids," he said. "We're realistic and I'd be surprised if there weren’t any offers for them, put it that way because they’re both extremely talented players.
"So I may have a decision to make but there’s been nothing for us to think about yet. For someone so young, Kieran already has vast experience - he’s played Champions League, Europa League, internationals and he’s won trophies.
"I don't think he would fear going anywhere but, personally, it would be a wrench for him because the club means so much to him. However, we’ll cross that bridge if and when we come to it but we don’t want to lose him."
It was reported last summer that Everton were prepared to launch a £25-million bid for Tierney but backed off with the understanding that the defender was reluctant to leave Celtic.
Tierney was limited to just 21 league appearances last term because of a hernia injury.