The Blues have already reportedly agreed personal terms with Zenit St Petersburg star Paredes, 24, as they search for Cesc Fabregas' replacement.
A four-and-a-half-year contract worth £80,000 a week has been drawn up and is ready to be signed once a fee is agreed.
Chelsea are confident in landing Paredes – who Zenit value at £36m – after upping their initial £26.8m offer, according to the Evening Standard.
Cagliari's £45m ace Barella, 21, was Maurizio Sarri's first choice to bring in as back-up to Jorginho but the Italian club have scuppered any chance of a January deal.
Mario Passetti, Cagliari's sporting director, said: "He’ll stay for at least the next six months.
"After that we’ll see what happens. Selling him isn’t one of our objectives.”
Fabregas joined Monaco last week leaving Sarri short of midfield options.
When asked if Chelsea will sign a replacement, the Italian boss said: "I have no idea.
"The club knows very well my opinion. I need a player there so it depends on the club's decision.
"I cannot do any more."
Meanwhile, misfiring Chelsea striker Alvaro Morata's exit is "in the balance" with Atletico Madrid only willing to sign him on loan.
The Blues are hoping to offload Morata, 26, in order to bring in a new striker, with Gonzalo Higuain and Callum Wilson the top targets.
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