The Gunners are a long way short of that valuation at present, with the bidding opened at just £15m ($19m).
That approach was knocked back, with the Scottish champions making it clear that they value a 22-year-old defender much higher than that.
Sutton believes Arsenal should be forced to dig a lot deeper if they really want Tierney, with Aaron Wan Bissaka’s £50m ($63m) switch to Manchester United having raised the transfer bar once more.
The former Bhoys striker told the Daily Record: “Kieran Tierney should be insulted by Arsenal’s bids for him.
“Celtic and Scottish football should also be seeing disrespect in what the Gunners are offering.
"Yet again I’m having the same argument I’ve been having year-on-year since Virgil van Dijk was inexplicably allowed to leave Celtic for a fee of £13 million in the summer of 2015.
“Nothing has changed. English clubs believed then they could get away with transfer market murder and they still do.
“Fair enough all clubs start low in a bidding process but £15m for Tierney smacks of disgusting contempt. Not just for Celtic and Scottish football but for the boy.
“If I were Tierney I would be wondering if they really rated me at all given the figures which are flying around south of the border.
“Both of those boys have had roughly one good season each in the English Premier League and that’s the fees?
“Are you trying to tell me that Chilwell is a four times better player than Tierney? Or that Wan-Bissaka is three times as good?”
Sutton added on Arsenal’s efforts to lure a highly-rated prospect away from Parkhead on the cheap: “Whatever way you look at it and however you see the level of the Scottish league, it’s nigh-on impossible to get to a final figure of £15m.
“It’s mocking Scottish football. It’s scornful to Celtic and disrespectful to the player.
“There is a halfway house here. Arsenal think they can get Tierney for around £20m. Wan Bissaka has gone for £50m.
“That means the meet in the middle figure should be at the £35m mark.
“And, if Celtic accept anything significantly less than that for Tierney during this transfer window, then they have been insulted again just as they were over the sale of Van Dijk.”