The Italian has made no secret of his own desire to return to Serie A, and Tottenham have been working to find a buyer as the club looks to overhaul its squad following a difficult season that saw survival only secured in the final weeks of the campaign.
Inter Milan had been expected to bring Vicario in as a replacement for Yann Sommer, whose contract expires this summer.
At the end of April it appeared that Inter's interest in Vicario was cooling, with the club instead turning its attention to other candidates.
Inter are now closing in on a move for Ivan Provedel from Lazio, a deal that opens the door for Vicario to sign for a rival club instead.
Sky Sport Italia transfer journalist Gianluca Di Marzio reports that two of Inter's rivals have shown concrete interest in the 29-year-old goalkeeper.
Juventus and Napoli are the two clubs in question.
Juventus have long been searching for a replacement for Michele Di Gregorio and are expected to bring in a new goalkeeper this summer, having already seen an earlier approach for Liverpool's Alisson Becker turned down.
Emiliano Martinez is also on the club's wishlist, with personal terms already agreed between the two parties, though Aston Villa still need convincing to sell.
Should the deal for the Argentine prove impossible to complete, Juventus are expected to shift their focus to signing Vicario instead, according to the reports.
Napoli's pursuit is more contingent, with the club first needing one of current goalkeepers Alex Meret or Vanja Milinkovic-Savic to depart before opening formal talks for Vicario.
Vicario's contract with Tottenham runs until the summer of 2028, but manager Roberto De Zerbi has already made clear his priority is to bring in his own choice as the club's long-term number one this summer.