The Spanish defender is set to join Inter on a two-year loan deal with the Italian club having an eight million euro option to make his move permanent.
Inter posted a photo of Montoya on the club’s official website with a caption: “Here is Montoya undergoing a medical.”
Montoya, a youth product of Barcelona, has made 43 appearances for the Blaugrana since breaking into the first team in 2011.
The 24-year-old, who is under contract with Barca until June 2018, made just 12 appearances for the Catalan giants in 2014-15 and is keen to leave the Nou Camp in search of more playing time.
“I’m sad to be leaving but (Barca coach) Luis Enrique told me he wouldn’t be relying on me,” Montoya said to the Spanish press. “I’m going on loan for two years but I hope I can come back.
“I realised I had to leave when the club announced they had renewed Dani Alves’ contract and signed Aleix Vidal (from Sevilla).”
Inter have already strengthened their defensive line with the arrival of Brazil centre back Joao Miranda from Atletico Madrid.
The Nerazzurri also acquired France midfielder Geoffrey Kondogbia from Monaco last week.
Inter, coached by Roberto Mancini, are looking to bounce back from a disappointing 2014-15 campaign which saw them finish eighth in Serie A to miss out on European football.