No players have been offered as part of the proposed deal, and the bid will be rejected by Palace.
The 26-year-old is keen to leave the club this summer and favours a move to Arsenal, but the Eagles value the Ivory Coast international at up to £80m.
The Gunners will have to hope a compromise can be reached on a lower fee and staggered payments.
Arsenal's summer transfer budget has been restricted by their failure to qualify for next season's Champions League.
After an unsuccessful move to Manchester United, Zaha made a permanent return to Palace in 2015 and has four years left on his contract, which he signed last summer.
Since he helped Palace earn promotion back to the Premier League in 2012-13, they have finished in the top half just once, coming 10th in 2014-15, when Zaha had returned on a season-long loan from United.
Zaha's brother, Judicael, told Sky Sports News: "Given all that Wilfried has given to Crystal 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."
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