Everton are prepared to sell Beto in January.
Tuttosport says Torino have made an approach and been encouraged by Everton to bid for the centre-forward.
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The Blues are seeking an outright sale for around €20m, having invested €30m in originally signing him from Udinese.
However, Toro president Urbano Cairo would prefer an initial loan with the option to buy in June.
Cairo is willing to put €3-4m on the table to take Beto on-loan in January, with an offer to also cover the majority percentage of his wages.