Milan vice-president Adriano Galliani says the Arsenal captain will sign for another club, while West Ham tell Stoke to up their offer for Carlton Cole.
Transfer talk: AC Milan 'rule themselves out' of Fabregas race
The Italian champions had expressed an interest in acquiring the 24-year-old's services this summer, but reports in Spain claim that Barca are close to securing the midfielder's signature after increasing their initial offer to £35 million (Dh205.3m)
"Fabregas will not join us because he will join a different club," Adriano Galliani, the AC Milan vice-president, told the club's official website.
The Potters are reported to have made an opening bid of £3m, plus various extra clauses, for the 27-year-old.
Allardyce accepts the Hammers have to look at balancing the books after their relegation from the Premier League last season but stressed players would not be allowed to leave cheaply.
"I believe at this stage that the offer is not good enough. It is not to the club's valuation," the West Ham boss told The Sentinel. "We are keen to keep our key players. However, we have lost our Premier League status and our financial position has to be addressed.
"A part of that might be players are sold back to the Premier League, but only so long as that is right for our club."
Demy de Zeeuw, the Ajax midfielder, claims he is set for a move to Spartak Moscow.
The 28-year-old has commented on his Twitter account that he will undergo a medical with the Russian club before signing a three-year contract.
De Zeeuw, who featured in 27 games for the Amsterdam club as they secured the 2010/11 Eredivisie title, said: "In the next few days I will have a medical examination and if that goes well I'm leaving Ajax for three years at Spartak Moscow.