The Gunners have been linked with the Scotland international for some time.
Interest is said to have been stepped up during the current transfer window, with a formal offer reportedly tabled this week.
An approach from Arsenal is said to have been knocked back, with Celtic valuing their 22-year-old academy graduate much higher than those in north London.
Former Bhoys and Gunners striker Hartson is not surprised to see that stance being taken, with the Welshman writing on Twitter: “My old club Arsenal testing the waters with reported £15m bid for Kieran Tierney.
“Celtic don’t want to sell besides that in this current market £15m is an embarrassment to the player and his ability.”
Hartson is not the only one to have hit out at Arsenal and their apparent reluctance to pay the going rate for a player of Tierney’s ability.
McFadden, a former international colleague of the highly-rated left-back, told BBC Sportsround : “[Virgil] van Dijk moves down for £13 million plus his sell-on clause then goes for £75 million. I think Kieran Tierney's certainly at that level.
“We're not talking about him going to a smaller side to build himself up. It's one of the top sides in England coming and saying we're going to take your best player for a pittance."
McFadden added on Tierney’s talent : “He's so level-headed, he's a funny guy, but when he trains, as you could imagine, he does everything to his best you know.
“You look at small things, when they do the wee sprints to warm up, he sprints his fastest.
“He puts everything into every session, and that transfers onto the game. It didn't surprise me the level of intensity of his training, and it's not a surprise that teams have come in. We've already said the bid is unacceptable, if that's the level they're going in at.
“There's no doubt that he would make it down there. It was a problem we had trying to pick a Scotland side, because you've got two of the best left-backs in the world, and that's not trying to make players feel better, that was the hard facts.
“Him and Andy Robertson, it’s difficult to split them. He'll go down there no problem. Andy Robertson, Van Dijk, Wanyama, these guys went to smaller clubs to show people that they can play at a higher level.
“He'll go straight down into one of the top clubs no problem. There's still improvement in him as well, that's the thing. He's a young guy and he can improve.
“He's the top man at Celtic. They can play without a guy in front of him because he can control the whole left side, going forward and defensively.
“When you go and play with better players it makes you better. You have to rise to that level, and it makes you a better player.
“Kieran Tierney is Celtic daft, so it'll take something phenomenal for him to consider it, and also for Celtic to consider it.
“I think it would need to take someone who's going to compete for a title in England or go and try to win the Champions League for Kieran Tierney to leave, because he's winning trophies, he's playing in Europe, he's playing for the club he loves.
“I think it would have to be something really special, and Arsenal at the minute won't challenge for the title. They might further down the line if they can invest in their squad, but £100 million is nothing in England.
“I don't think Arsenal will blow him away and make him think ‘I have to go and sign for Arsenal’.
“Arsenal look like they're trying to do things on the cheap, and if it's £15 million it proves they're trying to sign as many players as they can for as little as possible.
“It tells you that they're not ready to challenge for the title, and that's maybe in the back of Kieran Tierney's mind to say 'Why do I just want to go and try to finish sixth or break into the top four, when I could be winning titles for the club I love?'”