The Ivory Coast international has been linked with a move to the north London side from Crystal Palace in the summer transfer window.
However, the Gunners failed with an opening bid of £40m for the Palace winger as the Eagles look to secure a transfer fee in the region of £100m.
Arsenal have limited funds to spend on new signings in the current transfer window after the Gunners finished in fifth spot last term.
Unai Emery is thought to be eager to sign a winger to add more pace to the Arsenal team ahead of his second full season in charge.
Sky Sports News reporter Solhekol believes Zaha is doubtful about Arsenal’s ability to sign the Ivorian forward this summer.
Solhekol wrote on Twitter: “Source close to Wilfried Zaha says doubts about whether Arsenal can afford to sign him.
“Palace have rejected £40m Arsenal bid & they value Zaha at closer to £100m.
“Palace would not be interested in taking players as part of swap deal. Would only ever happen as last resort.”
Arsenal finished in fifth place in the Premier League table last term behind Chelsea FC and Tottenham Hotspur in the race to secure a Champions League spot.
The Gunners missed out on the chance to secure Champions League football last term by winning the Europa League title when they lost 4-1 to Chelsea FC in the final.
Arsenal have only signed South America teenager Gabriel Martinelli from Brazilian club Ituano in a £1.6m deal so far this summer.
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