Allardyce said: "We have had a look at him in training, but the problem is that he hasn't had a club since the start of the season so it's a question of how long it would take him to get up to speed.
"We might need someone against Coventry, as quickly as that."
With the Hammers having been hit by a wave of injuries and currently seeking defensive cover, Pavon could be in the squad as soon as Saturday for the clash against Coventry.
Source: DSG