Chelsea are also hot on the heels of Zenit St. Petersburg's Argentina midfielder Leonardo Paredes - as confirmed by Goal - as they look to fill the gap left by Cesc Fabregas.
But Cagliari director Mario Passetti has poured cold water on the prospect of Sarri landing Barella this season.
“We reiterate that he’ll stay for at least the next six months.
“After that, we’ll see what happens in the summer. We have big ambitions and Nicolo gives 1000 per cent in every training session and he’s happy to be at Cagliari.
“Selling him isn’t one of our objectives.”
Barella’s stock has risen rapidly since he became a mainstay in the Cagliari team.
He made his debut in 2014 but it was the 2015-16 season when the man from Sardinia made his breakthrough as a cornerstone of I Rossoblu.
Cagliari’s unyielding position will mean Sarri is forced to look for a plan B as he seeks a replacement for Fabregas who departed this month for Monaco.
Zenit have quoted Chelsea €40m (£36m/$46m) if they want to prize Paredes away from the Russians. The Blues' own valuation is believed to be some way below that figure at €30m (£27m/$34m).
Former Milan forward Antonio Cassano has suggested that Higuain is eager to be reunited at Stamford Bridge with his former Napoli coach Sarri as he is being starved of service at San Siro.
The Argentinean is believed to be Sarri’s priority buy ahead of Bournemouth striker Callum Wilson.
In December, Chelsea number two Gianfranco Zola confirmed that the England international was a player that the club were interested in, but Cherries boss Eddie Howe is understandably reluctant to sell.