The Hammers chief was forced to field a backline devoid of an orthodox centre-back for much of his side’s weekend draw with West Brom, due to a number of injuries to some key first-team players.
As a result, ‘Big Sam’ is believed to be ready to delve into the winter market to ease his growing concerns, and has made Burdisso a top target.
The 32-year-old Argentine has struggled for playing time at Roma this term, which may see his chances of representing his nation at next summer’s World Cup evaporate as the season goes on.
Burdisso’s current contract expires in a little over six months’ time, meaning that a cut-price swoop once the transfer window re-opens is a possibility.
AC Milan are also keen, but Roma may be more willing to do business with a foreign side to avoid strengthening a domestic rival.
As well as this, Allardyce is thought to be looking for a new striker with Andy Carroll currently sidelined through injury.