Inter are seeking a replacement for veteran Yann Sommer, who will leave when his contract expires at the end of June - and Vicario is their priority target.
Pagliuca told TMW: "Inter need a strong goalkeeper, and Vicario is that. He played in the world's top league and for a team that until recently was aiming to win the Premier League.
"He couldn't turn down Tottenham, especially after a Champions League final. This year he's had difficulties, but the whole team has had them, and they've changed coaches.
"He's one of the best Italian goalkeepers around. He's not yet a top player, but if Inter sign him, they'll do so for his quality, not because he's Italian. In recent years, they've always chosen the best they could afford.
"He's very good in goal, but he needs to improve his exits; sometimes he stays too close to the line. It would be a new challenge for a top Italian team, but he can do it."