The Italian international, who began his career with the Sardinians, has been heavily linked with a switch to the San Siro, and talks between the Nerazzurri and the player’s agent are believed to have taken place.
Reports earlier this week suggested Inter had agreed terms with the 22-year-old, however their valuation of the player appeared to fall short of Cagliari’s asking price of between €45 million and €50m (£44m/$56m).
While his transfer fee remains a potential sticking point, there is also a suggestion that Inter defender Alessandro Bastoni could be factored into the deal following a successful loan spell with Parma.
Speaking to the media from Italy’s Coverciano base ahead of their Euro 2020 qualifying double-header against Greece and Bosnia and Herzegovina, Barella claimed a move this summer is a possibility – but his thoughts are currently on playing for his country.
“It may be [that I leave Cagliari],” he told reporters. “It’s nice, but I don’t think about it.
“The market is open for me. It may be that I leave, but for now I’m focused on the national team.”
Barella has emerged as one of Serie A’s best young midfielders, and has also been linked with a move to the Premier League after earning praise from the likes of Andrea Pirlo and Alessandro Del Piero.
His versatility has caught the eye of a number of clubs, but Inter remain in pole position to secure his signature having opened a dialogue with Cagliari.
For all the talk, however, Barella says he is remaining calm and pouring all of his efforts into representing Italy over the next week.
“I’ve put my phone on silent,” he said. “This is our job and we need to stay focused.
“My line of thinking is shared by me, [Federico] Chiesa, [Moise] Kean, [Nicolo] Zaniolo and many others.
“We’re not thinking about the market. It may be that we’ll be on the move as it’s all open, but we’re only think about playing.
“I said goodbye to my team-mates like all the other years when I was extra certain of staying at Cagliari. I live everything calmly.”