The Euro 2016 winner made a change of agent recently, leaving Jorge Mendes for Joorabchian, who is known to be more 'aggressive' in the market for his clients.
"A European champion must be rewarded. From now on, we either discuss a new contract or the sale to another club," the Iranian told Record.
"Sporting received four offers. Inter Milan and Liverpool, certainly, with amounts between 35 and 40 million, plus bonuses. Sporting turned down all bids."
According to the Portuguese publication, the two other sides who made bids for the 23-year-old were Chelsea and Ligue 1 Champions Paris Saint-Germain.
Mario has scored 14 goals and registered 17 assists in 92 games for Sporting and currently holds a €60m release clause in his contract.