The former Stoke City striker could bolster Palace's forward line as they try to avoid the drop this season.
Allardyce currently has Christian Benteke and Fraizer Campbell at his disposal, while Bakary Sako is pushing for a first-team spot.
Connor Wickham is still out injured and Loic Remy is on his way back from injury and could make his debut against Bolton this weekend. With that in mind, Allardyce is tempted to give Moult a chance following his successful spell at Motherwell.
The former Aldershot, Nuneaton and Wrexham star has scored 11 goals in 18 appearances for the club this season and Allardyce believes he could make a big difference in their bid to avoid relegation.