The Gunners have seen a first official bid turned down for the German midfielder this week and, while Mikel Arteta is believed to still be keen to bring him to the Emirates Stadium, the move has left many Gunners fans puzzled.
Havertz scored the winning goal for Chelsea in their 2021 Champions League final victory over Man City, but on the whole he has failed to really deliver since his £75million arrival from Bayer Leverkusen.
The Blues are thought to be open to selling him but want more than the £50m offer Arsenal proposed, which was rejected on Friday evening, while Bayern Munich have now joined the race.
Arteta's pursuit of the 24-year-old has raised eyebrows with some supporters, with many questioning if he's worth the money.
Former Chelsea defender and regular Blues pundit Jason Cundy was asked that very question by Andy Goldstein on talkSPORT's Drivetime show, and he didn't seem overly convinced by the Germany international.
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"I've covered pretty much every game Havertz has played for Chelsea, and he's a curious one," said the talkSPORT host and pundit.
"Look, he scored the winning goal in the Champions League final, so he can do it, there is no doubting his ability, technically he's a brilliant footballer.
"But how many times as a Chelsea fan can I look back and go, 'Kai Havertz today, wow'? Not many.
"He reminds me of Mesut Ozil. He's got his languid playing style. It doesn't look like he cares. He's a stroller around the pitch.
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"The thing that would concern me if I was an Arsenal fan is he goes missing. He lacks a bit of heart, a bit of steel, a bit of fight and he can drift out of games very quickly. If you're in a battle I'm not sure he's the man you want.
"I think the trial may have finished for Havertz at Chelsea. I think they'll probably say, 'We've seen enough of this, it hasn't quite worked, move him on'.
"And I don't think there are too many Chelsea fans out there who are worried about this move. I think anything over £60m would be a decent fee."
The main question Arsenal fans are asking, though, is where Havertz would fit in their team.
Martin Odegaard has excelled this season as Arsenal's creative commander-in-chief, with his stellar performances and presence in the team seeing him named club captain.
Cundy believes Arteta may see Havertz as another star-in-the-making similar to Odegaard, with the boss helping to unlock the Norwegian's long foreseen full potential after being outcast at Real Madrid.
But he admits there is still a major question mark over the German's best position, and whether a move to the Emirates Stadium would actually work.
"In what system do you play Havertz? I don't know," added the former Blues defender.
"He's not a No.9, he's not a frontman, he's a No.10 for me - but the system has got to suit him, as opposed to him fitting into a system that's already there and it works.
"I've got some sympathy with him, because I don't think Chelsea have played him in his best position, and that's partly down to the fact Chelsea haven't had a No.9, so he's filled in.
"He's got to play off a frontman, that would be the best for him. For example if you had Didier Drogba up top and you played Havertz in behind him.
"Arsenal last year played 4-3-3, where would Havertz fit in that? How would Havertz and Martin Odegaard fit in the same team? If Arsenal sign him, I think Arteta would have to change the system.
"I'm not saying he wouldn't succeed at Arsenal. Arteta might be looking at him and thinking, 'Chelsea have let him down… I can get something out of him, I know the player that's in there'.
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"Look at Odegaard now and where he was two years ago. Nobody saw him becoming the player he is now.
"Arteta has turned him into one of the best creative midfielders in the country, so maybe he's looked at Havertz and thinks he can do the same with him."