Barbosa impressed for Santos last season and earned a call up to the Brazil squad for the Copa America and Rio Olympics.
Chelsea have been linked with the 19-year-old and Brazilian publication Globo Esporteclaimed last month he was tempted by a move to Stamford Bridge.
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Inter Milan have made a bid for Gabriel Barbosa
However, Barbosa's agent Wagner Ribeiro has now revealed Inter have made an offer for the winger.
"Inter have made an official offer of €25m [£21m] for the complete economic and sporting rights of Gabigol," Ribeiro told Brazilian newspaper Lance.
“For now we want to leave Gabriel in peace. Inter’s is the third official offer that Santos have received for Gabigol.
“When the Olympics finish with the gold medal - God willing - we’ll sit round the table and resolve his future. We’re calm.
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“When the Olympics finish I’ll sit down with Gabigol and his family and decide his future.”
Barbosa is under contract with Santos until August 2021.