The Nerazzurri are looking at a number of candidates to replace the former Slovenian international and the Argentine was integral to the Zebrette surviving relegation in 2019/20.
According to Tuttosport, Udinese want at least €30 million for Musso and they are unlikely to lower that price tag for Inter.
Other options in Serie A that the Biscione have been looking at include Alex Meret, who is second choice to David Ospina at Napoli but still valued at €40-50m, and Cagliari goalkeeper Alessio Cragno, who would cost no less than €25 million.
Inter will also be keeping an eye on 20-year-old Brazilian Gabriel Brazao, who is on loan at Spanish club Real Oviedo.
Musso has played in 73 competitive matches for Udinese since his arrival in the summer of 2018 and he has kept 22 clean sheets, with 14 of them coming in the 2019/20 Serie A season.