Eagles boss Dougie Freedman is keen to bolster his squad before the close of the transfer window and is keen on luring Allan to Selhurst Park.
Allan, who joined West Brom last January from Dundee United, is highly-regarded at The Hawthorns, but is is regarded as very much one for the future.
The attacking midfielder is likely to find himself down the pecking order at The Hawthorns this season and the Baggies could be willing to loan him out so that he can get some regular first-team action.
The 20-year-old enjoyed a successful spell out on loan at Portsmouth last season, impressing during his stint at Fratton Park.
A number of clubs are thought to have made enquiries to sign Allan on loan, but Palace are hoping to win the race for the Scotland Under 21 international