Chelsea boss Antonio Conte wants a decision from Roma striker Edin Dzeko by Monday.
The Telegraph says Conte is ready to pull the plug at the end of the weekend in order to pursue other targets before Wednesday's transfer deadline.
Chelsea have already agreed a deal to sign Roma left-back Emerson Palmieri, 23, and were hoping to wrap up a deal for teammate Dzeko, 31, as well.
However, Roma have made it clear they would prefer not to sell, while the former Manchester City star is believed to be demanding unrealistic contract terms.
But Conte is desperate to land a powerful target man and believes Dzeko would provide the quality necessary to boost Chelsea's top four hopes.
It's said that the Blues are in fresh talks with Roma as they look to negotiate a transfer fee.