According to a report from Italian outlet Tuttomercatoweb, Roma are considering a move for Vestergaard, despite Spurs being seen as the favourites for the defender.
The Danish defender is high on Tottenham's shortlist for the summer, as they look to strengthen their defence after another disappointing season.
However, Roma are keen on signing Vestergaard, wanting an 'experienced and quality' defender next season, with Roma's director Tiago Pinto already planning to start talks with Vestergaard's agent in the coming week.
The Italian outlet is also claiming that Vestergaard has emerged as a potential transfer option for Juventus, who are keen on overhauling their squad after failing to challenge for the title this season.
The 28-year-old arrived at Southampton from Borussia Monchengladbach in 2018 for £18 million, being a key player for Ralph Hasenhuttl's team this season.
Vestergaard helped Southampton up to seventh place in the Premier League before sustaining a knee injury in December, leading to the Saints suffering from a downturn in form since the start of the calendar year, with just three league wins since 2021 started.
Apart from Vestergaard, Spurs have also been linked with Inter's Milan Skriniar, yet they failed to sign him in January, and it remains to be seen whether they will be moving in for him now that Jose Mourinho has been sacked.