The 31-year-old, a free agent after leaving French side Arles-Avignon, has been training with the Hammers after they were hit with a spate of injuries.
Hammers time: Francisco Pavon (right) is trying to secure a deal
'We have had a look at him in training,' said Allardyce.
'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.
'We have a three-game week coming up and we might need someone for that. Ability-wise, Franco would certainly be capable but physically, because he hasn't had a club for a while, that fitness is way down. We haven't written it off yet.'
Allardyce has already failed in a loan move for Arsenal defender Sebastien Squillaci.
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