After moving to Lazio on a free transfer from AZ Alkmaar in 2015, the 23-year old made his international debut for the Netherlands following a string of impressive performances.
Hoedt made 21 league appearances for Lazio last season, scoring 3 goals, but watched on from the bench as his side defeated Juventus 3-2 in the Italian Super Cup on Sunday.
Hoedt could still line up alongside his compatriot Virgil van Dijk, with Ralph Krueger, the Southampton chairman, maintining that the wantaway Dutch player will not be sold despite submitting a transfer request last week.
If he does end up joining the Saints, he will be their fourth signing this summer following the aquisition of Mario Lemina, Jad Bednarek and 16-year old Will Ferry from Juventus, Gornik Leczna and Bury respectively.
Earlier this week Southampton announced that an 80 per cent stake in the club had been purchased by Chinese businessman Jishen Gao.