Beattie enjoyed a productive loan spell at Palace last season, scoring five goals in 15 appearances before finishing the campaign with Sheffield United.
Warnock was keen to lure the Scotland international back to Selhurst Park and was hoping to sign the 25-year-old on a season-long loan.
However, he has revealed that the Baggies are only willing to sell Beattie, with Palace unable to afford a permanent deal.
"We have spoken to West Brom about the prospect of bringing Craig back here," Warnock told the Croydon Advertiser.
"But they said they would only do a permanent deal and we can't afford that."
Meanwhile, Warnock has insisted Nick Carle is part of his plans after South Korean side FC Seoul made an approach to sign the Australian midfielder on loan.
Warnock said: "A club have come in for Nick, but we don't want to let him go - he is part of our plans here."