Off contract in June, Mata is considering his options at United, which hold a 12-month option in his deal.
La Repubblica says Lazio sports chief Igli Tare has made a first approach to Mata and tabled a pre-contract offer to the veteran.
Tare has offered the 33-year-old a two-year contract worth €4m-a-season.
Mata is keen on a move to Rome, though his counter proposal is for €5m-a-season.
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