The Brazilian midfielder spent the second half of last season on loan at San Siro, where the Nerazzurri possessed the option to buy Rafinha this summer for £30m - an option that Inter rejected the chance to activate.
However, Inter are interested in signing the 25-year-old on another loan deal, according to Mundo Deportivo (via Football Italia). One sticking point for the Italian club is that Barcelona are demanding an obligation to buy Rafinha is included in the season-long deal.
It is known that the Brazil international, who is the brother of Bayern Munich midfielder Thiago Alcântara and the cousin of Valencia's Rodrigo, is keen on returning to Inter this summer.
But the player's agent recently admitted he had already been in contact with other clubs.
"We couldn’t afford to wait any longer (for Inter), now it’s only right for us to look around," agent Marzinho told Gazetta dello Sport.
"He loved it at Inter, he adapted immediately and the fans took to him with affection and enthusiasm. Unfortunately, we’ve had no signals from the club. It’s a shame because it would’ve been a chance to play for Inter in Europe after conquering it on the pitch. The agreement with Barça expired on June 5.
"My son would go back even now, but it’s been too long. If they’d wanted to take it seriously they would have moved with conviction. Now it’s important to choose someone else. We’re evaluating, the phone is ringing. There have been requests from La Liga, the Premier League, Ligue 1 and the Bundesliga."
Inter have already spent big this summer, splashing almost £65m on just four signings. Radja Nainggolan joined the club from AS Roma, while Matteo Politano moved to San Siro from Sassuolo.
Argentine striker Lautaro Martinez and Italian defender Federico Dimarco have joined from outside of Serie A.
However, Inter's most impressive business this summer has been a double deal to sign Kwadwo Asamoah and Stefan de Vrij on free transfers from domestic rivals Juventus and Lazio respectively.