The former Hammers striker has been linked with a number of clubs since he was suspended by Manchester City for allegedly refusing to warm up against Bayern Munich last month.
Allardyce had said that he would welcome the Argentinian back to Upton Park.
"I don't think [the Tevez deal] has got any more potential now," he told BBC London.
"We've invited El-Hadji Diouf in for a bit of training to see what level he lies at," he added.
"We all know certain players have different sets of baggage, but for me that quality and outstanding ability mean the baggage is minimal.
"[We will see] if he's capable of reproducing the top form that he's done for me at other clubs."
Allardyce has worked with the Senegalese forward at Bolton and Blackburn.