The highly-rated left-back has emerged as a top target at the Emirates.
A first bid worth £15m went in last week but was rejected by the Hoops.
And reports have suggested a second offer of around the £18m mark has since been turned down too.
Tierney would provide a long-term solution for Unai Emery in defence given he is just 22 years old.
Celtic have shown their huge faith in the Celtic Park star, having handed him a six-year contract back in October 2017.
He is already one of the squad’s highest earners, but Arsenal are looking to provide him with another significant pay boost.
According to The Scottish Sun, Arsenal are willing to pay Tierney more than £70,000-a-week, which equates to £4m annually.
Over a five-year deal, which would tie Tierney down in north London until 2024, he would receive a whopping £20m.
“A minimum of £25m is being demanded for Tierney”
That would dwarf the money he would be getting at Celtic, who face the prospect of losing the Scotland skipper.
The Scottish champions are prepared to play hardball over a fee, though,
Tierney is currently sidelined following a double hernia operation, although he should be available come the start of the new season in August.
Whether that will be in the Scottish Premiership, the Premier League or Serie A – with Napoli also interested – remains to be seen.
Arsenal are expected to press ahead in their efforts to agree a deal, though.
And should Tierney join the Gunners, he will be on the same pay as the likes of first-team regulars Lucas Torreira and Shkodran Mustafi.