The Bolton manager is heading the hunt for the Romanian star who can play as a defensive midfielder or a centre-half.
Allardyce is also closer to landing Roma midfielder Olivier Dacourt. The Sunday Mirror says Allardyce can clinch Dacourt's signing if they can beat the £15,000-a-week wage offer that Roma have tabled to keep the Frenchman in Italy.
Meanwhile, Bolton and Blackburn are interested in Roeselare youngster Tom Raes.
The defensive midfielder has been offered a two-year pro deal by his Belgian club, but his advisors are also fielding offers from abroad.
Along with Bolton and Blackburn, Serie A outfit Lazio have made a serious move for Raes, offering him trials after scouts spotted him in a youth tournament this year in Rome.
Chelsea have also been following 18 year-old Raes for the past two years.
Trotters boss Sam Allardyce has also refused to rule out a summer move for on-loan Japanese midfielder Hidetoshi Nakata.
Newspaper reports have speculated about the possibility of Charlton bidding for Nakata, but Allardyce believes that both he and Alan Curbishley may struggle to reach a financial agreement with the playmaker after he took a substantial wage cut to move to England in the first place.
"I wouldn't have thought so (Nakata to Charlton)," Allardyce told Sky Sports News. "I'd have thought it's just pure press speculation because he had a really good game here.
"We've found out he might be available for a move from Fiorentina at the end of the season.
"That's a difficult task not only for Charlton if they want him but also for us because he is moving into the last year of his contract.
"Whether the financial demands could be met with Hide is probably the biggest problem and like everything else, limits us managers, particularly me and the likes of Curbishley, to sometimes not being able to get someone like Hide.
"When we got him, Hide and his agent worked tirelessly to get the financial package to the right amount of money for Bolton Wanderers."