The 24-year-old striker has yet to be on the losing side in three matches for Palace and scored a memorable winner in the recent south London derby win over Charlton.
His initial one-month loan spell ends following the home game against Nottingham Forest on October 28, but Warnock has already been in touch with West Brom counterpart Tony Mowbray over a possible extension.
"We sincerely hope we can keep Craig beyond the month and I know Neil has spoken to Tony Mowbray about it already," assistant-manager Mick Jones told the South London Press.
"We might get news on that sooner rather than later. Craig has had a big effect on the training ground and in the dressing room."