The former AC Milan and Barcelona forward, who is a free agent after leaving Brazil's Cruzeiro in February, has returned home after last week's talks with the premier league club.
Allardyce, who is still waiting for an answer from the 32-year-old, told Thursday's Bolton Evening News: "At this time of year, nobody wants to make a decision, but we will be asking for a decision either way before very long.
"We are wise enough to know what's going on behind the scenes.
"We're probably being used to create interest from elsewhere. You'd be surprised how many other football clubs it kick-starts into action.
"I'm disappointed we haven't got a decision yet," he added. "That tells me there is still hope, but there will have to be a movement from his Brazilian agents soon.
"If there isn't a positive move in a few days, we will have to call time on it."
A former World Player of the Year, Rivaldo would be an even bigger coup for Allardyce, who has recruited French World Cup winner Youri Djorkaeff and Nigeria captain Austin 'Jay-Jay' Okocha to a club that has battled against relegation in past seasons.
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