Palace made their own pitch at around £150,000 a week and rising for their talisman, who will give them an answer in the next few weeks.
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Jet-heeled forward Zaha, 30, has had plenty of foreign interest and Al Sadd are willing to put him in the £200,000-a-week pay category.
So the Eagles hero — out of contract at the end of this month — must decide whether to chase more money or settle with what he can get at Selhurst Park.
Zaha scored seven goals in 28 league outings for Palace this season.
The South London side’s struggles under Patrick Vieira saw Palace ranked as one of the worst attacking teams in the division before Roy Hodgson swooped in to fly the Eagles to safety.
In the season prior Zaha had managed his best-ever return with 14 league goals.
Overall, the Ivory Coast International has netted 68 league goals for Palace, adding 42 assists as well.
The likes of Arsenal and Chelsea have both been linked with a move for the forward in the past.
However, the £10m-plus contract offer from Qatar may prove to be too tempting.
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Zaha has transferred away from Palace before, though his move to Manchester United in 2013 proved to be a dub.
He struggled for game time there under David Moyes, he then found himself on loan at Cardiff before being sold back to Palace in 2015.