The talented midfielder, who starred for Portugal at Euro 2016, has been linked with a move away from his homeland.
Chelsea and Liverpool have both expressed interest and according to Portuguese newspaper Jornal De Noticias, Mario's agent Kia Joorabchian has informed Sporting of Chelsea's £39m bid.
Inter Milan are also thought to have made an offer, but the report suggests the Blues are leading the chase as they are willing to pay more upfront.
The Gunners are in desperate need of defensive reinforcements and the Germany international is set to complete a £30m move to the Emirates.
Express Sport understands a deal will be completed in the next 24 hours.
Jose Mourinho has reportedly been told he will not be able to make any more signings until he sells some players.
The Portuguese tactician is still keen to bring in another defender despite already signing Eric Bailly.
But ESPN claim United officials have told Mourinho that he won't receive any funding for transfers if he doesn't create space within his squad.
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