Chelsea and Tottenham have both been strongly linked, but Brazilian sources put the European champions firmly in pole position for the 20-year-old midfielder.
And now Inter chief Giovanni Luigi has revealed that they want any deal for Oscar to smash the Brazilian record, and Chelsea are close to this.
"I want the transfer of Oscar to be the biggest transfer deal ever in Brazilian football," Luigi told Radio Gaucha.
"And the Chelsea offer isn't that far from that."
However, Luigi admitted that they would have no qualms about keeping Oscar - just as they did with Leandro Damiao.
"Last year Tottenham made two offers for Leandro Damiao. We kept him and he was very important," he continued.
"He is Internacional's top scorer in Libertadores and Brazil's national team number 9.
"Oscar's situation is similar. I'm part of an administration that has always been competent to replace those players that leave.
"If regarding Oscar we get offers that match our expectations, we'll negotiate.
"But they have to be of the value that mean significant resources for Internacional. But those values would be the biggest negotiation in Internacional's history."
Luigi also confirmed that the club are aware of Ganso's link to the club - as the midfielder looks set to quit Santos.
And whilst confirming their interest, he admitted he does not think the deal will happen.
"When I talked to him, he told me that his relation with Santos' board has been bad for a while. Delcir Sonda's [whose company owns 50 per cent of the player] information is that he was unhappy.
"If Santos were willing to sell their part, there would be two options: selling him abroad or move him to Internacional.
"This is a possibility, but a very remote one. I don't believe in that possibility.
"Sonda is a die-hard Internacional fan and overexcited at times. So he ended up talking about that in an interview. But I can tell you that this possibility is very hard."
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
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