Chelsea are reportedly in the mix to sign Allison.
The Brazil keeper was said to be close to sealing a switch from Roma to Real Madrid once the World Cup is over.
But, according to Marca, Chelsea could be willing to shell out an amount close to Roma’s 70m euro (£62m) valuation.
A move from Blues would suggest that they fear Thibaut Courtois is set to leave.
Courtois is in Real’s sights and out of contract at the end of next summer.
The European champions have courted several replacements for Keylor Navas, including Athletic Bilbao keeper Kepa Arrizabalaga and Manchester United’s David De Gea.
But Arrizabalaga signed a seven-year contract in January and United have no intention of selling De Gea.
And Blues may now fear that Courtois could be on his way to the Spanish capital if Real can’t agree a deal with Roma.
Marca say that Real have offered 40m euros (£35m) for Allison.
But Roma have rejected that bid are said to be unwilling to break the bank to get their man.
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