Celta had a fixed option to buy Rafinha, 27, for €16m at the end of his loan stint.
But the Galician club set a ceiling of €10m and that hasn’t been enough to convince Barca.
Barcelona reduced Rafinha’s release clause from €75m to €16m in order to facilitate an exit while making money.
Sources of the Catalan side have told Mundo Deportivo that Italy’s Serie A is now the most likely destination for Rafinha.
Rafinha spent half of the 2017-18 season on loan at Inter and the Nerazzurri still have an interest in him.
Inter could return for Rafinha, although any deal would be separate from negotiations for Lautaro Martinez.
Last summer, Premier League clubs came calling for Rafinha, but this year they are silent.
The two-time Brazil international is enjoying a few days on vacation and will consider his options.
Rafinha wants to play in the Champions League next season, something Inter would be able to offer.
Celta are not likely to improve on their offer of €10m, essentially ruling them out of the race.