Portuguese newspaper A Bola state that Milan are currently leading the race for the Argentina international and sent scouts to run the rule over his performance in Benfica's 3-2 win over Estoril on Saturday.
United and Liverpool keeping tabs
However, the Express maintain that both United and Liverpool are keeping tabs on Salvio, with a view to securing his services in the New Year.
Hamburg and Valladolid are also interested, as are oil-rich AS Monaco, who could match anything offered to Salvio from elsewhere in terms of wages.
Benfica want £34m
Arsenal, Manchester City and Tottenham were linked with the winger last year, but the Premier League trio were deterred from making an offer after being quoted a cool £34 million by Benfica.
At the time his agent, Agustin Jimenez, confirmed that while Salvio was happy at the Estádio da Luz, his client was open to a move away from the Portuguese giants.
"After a big season it is normal that significant clubs will be interested," he told reporters. "Now the decision is in the hands of Benfica. Salvio is content at the club but he is open to the possibility of a move."
Salvio, who spent two years with Atletico Madrid before sealing a move to Benfica in 2012, has made five appearances for the Argentina national team but was not part of the Albicelestes' 2014 World Cup squad.
Do United and Liverpool need him?
Whether Manchester United require another winger is debatable. Louis van Gaal's current system favours full-backs over traditional wingers, with record signing Angel di Maria deployed in a central role.
Liverpool play in a more conventional fashion, and Salvio might be regarded by manager Brendan Rodgers as the perfect right-sided winger to compliment Raheem Sterling on the opposite flank.
However, the Reds purchased Salvio's former Benfica teammate Lazar Markovic in the summer, and the 20-year-old is regarded as a potential key player at Anfield.
Whether Liverpool strengthen in January could depend on how they perform in the Premier League and Champions League between now and the New Year.
United, meanwhile, are expected to spend big against when the transfer window re-opens. However, their focus will be primarily on securing the services of another centre-back and potentially another central midfielder.