That is according to Gunners legend and ex-Barca forward Thierry Henry.
The Chile international’s own future at the Emirates remains uncertain amid his contract stand-off.
Express Sport understands Sanchez has demanded a staggering £400,000-a-week to sign on, with his current deal expiring in 2018.
However, Arsene Wenger has warned Arsenal will not be held to ransom, meaning they could well sell this summer.
Neymar and Alexis Sanchez spent a year together at Barcelona in the 2013/14 season
A shake up of the squad is expected, with a number of incomings being targeted.
But luring the world’s best is no longer within Arsenal’s capabilities, Henry admits.
If they were to go for the likes of Manchester United target Neymar via his connection with Alexis Sanchez, Henry does not see much reason for optimism as the message would no doubt be negative.
“Arsenal are not just up against the Barcas, Reals and Manchester Uniteds – now Juventus are back paying big fees, Paris Saint-Germain are spending,” Henry wrote in his column for The Sun.
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If Neymar called Sanchez tomorrow and said: ‘Should I join Arsenal?’ what would he say?
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“What can Arsenal put on the table to beat those teams to talent? It won’t help that there is uncertainty over the two star players in Mesut Ozil and Alexis Sanchez.
“Are they staying or going? Other players will look at that and wonder why they are hesitating to commit to the club.
“And, of course, players talk to each other. If Neymar called Sanchez tomorrow and said: ‘Should I join Arsenal?’ what would he say?
Neymar has achieved far greater success at Barcelona than Alexis Sanchez has with Arsenal
“You try to find out what a club is like. And when you’re with the national team it comes up.
“The feedback at the moment from Arsenal wouldn’t be great. You only need to look at the results to determine that.”
Neymar may leave Barca at the end of the season, with United, PSG and Manchester City among those who could be willing to match his £170million buy-out clause.
The Catalan giants are reportedly planning for life without Neymar, but moving to Arsenal is beyond unlikely in Henry’s eyes.