Juranovic further added to his reputation at the World Cup in Qatar as part of the Croatia squad and could be set to move from Celtic this month.
He has interest from a number of clubs, but it is Monza who are now putting in serious effort in order to agree a deal.
Monza are in talks to sign Juranovic on loan with an option to buy, according to Italian journalist Nicolo Schira.
The option to buy would turn into an obligation if Monza remain in Serie A this season.
Monza currently sit in 14th spot in the Serie A standings and boast an eight-point advantage over the bottom three.
Juranovic played for Celtic in their Glasgow derby draw with Rangers earlier this week, being brought on off the bench by boss Ange Postecoglou.
Celtic have the 27-year-old defender under contract until the summer of 2026.
