Unai Emery’s side have been linked with Zaha throughout the summer.
And the north London side could be moving nearer to a deal.
Shared on Twitter by Sky Sports News reporter Kaveh Solhekol, Zaha’s brother said: “Wilfried will always hold Crystal Palace and their fans in the highest regard and all the support they’ve given means the world to him.
“It’s my brother’s dream though, to play for Arsenal.
“Given all Wilfried has given to Palace to help them remain a Premier League club, I hope Palace will be able to see their way to agreeing a deal with Arsenal that allows Wilfried to realise his dream of playing European Football for the club he’s supported since childhood.”
The Ivorian scored 10 goals and made 10 assists for the Eagles last season, his ninth at the club.
He spent one season at Manchester United after helping Palace to Premier League promotion in 2014.
But the 26-year-old quickly returned to Selhurst Park to score 35 goals in 180 appearances.
Zaha has now been linked with a move to north London.
His price, though, has been set at £80m by the south London club with Arsenal some way off reaching their valuation.
And fans on Twitter have reacted to the Gunners’ bid – half that price – in a brutal way.
“Typical Arsenal,” one viewer said.
“That wouldn’t even buy his right leg.”
“Zaha? More like Haha”
Another commented: “Zaha? More like Haha.
While a third suggested the club’s recent business hugely impacts the bid.
“They’ve bid £40m after Palace sold Aaron Wan-Bissaka for £50m,” they said.
“Are they serious?”
Gunners rivals United confirmed the full-back’s signing last week.
A fourth added: “Arsenal are bantering.”
And a fifth suggested the north London side were already at their maximum price.
“That’s their entire transfer budge done and it’s not even Zaha’s price tag,” they said.
“Banter club at its best.”