According to Calciomercato.com, there are also several other sides showing an interest in the 18-year-old talent, but the three Italians seem more likely to complete a swoop.
The teenager has joint Irish and Albanian citizenship, and was born in Glasgow, but has chosen to represent the Republic of Ireland at various youth levels.
He already has two goals in a single cap for Ireland at Under-21 level, during a 3-0 win over San Marino in September.
His contract with Celtic is due to expire in March 2024, but a January move could also be possible for a small fee.
So far this season, Vata has already scored 10 goals in 14 competitive matches for the Celtic Reserves.
Inter had also shown an interest in Vata and could potentially work with one of these other Italian clubs in order to get the deal done.