The Yugoslavia international is believed to have decided against accepting the offer of a three-year contract from Jean Tigana's newly-promoted Premiership side, in order to play for Didier Deschamps' Le Championnat outfit.
After visiting Monaco on Tuesday evening, he has undergone the medical examination but the length of the deal is subject to clarification with some sources claiming it will be two years in duration, and others indicating it will be on loan for a year.
The 31-year-old defensive midfielder made 44 league and cup appearances for Inter and also represented Juventus, Lazio and Sampdoria during an eight-year stint in Italy, which was briefly interrupted when he played a season in Spain with Atletico Madrid.
A composed performer, Jugovic is one of a select band of players to have lifted the European Cup with two different sides - Red Star Belgrade in 1991 and Juventus in 1996.
Deschamps, a former team-mate of Jugovic at Juventus, is also pursuing Cyril Domoraud.
After a loan move to Bastia, the defender was transferred from Milan to Inter.
"I am very impatient," he said. "I hope it will be settled as soon as possible.
"Monaco is a very ambitious team that will compete for the top places in Le Championnat.
"I would really like this move. For the moment, I am waiting for both sides to negotiate but I believe the matter is going well."
Deschamps is also reportedly on the trail of Parma striker Patrick Mboma.
Meanwhile, Paolo Costa is also exiting the Guiseppe Meazza, as the Portuguese playmaker is expected to be sold to Benfica in a part-ownership arrangement.
The midfielder has been with Reggina but was recalled, albeit briefly, by Inter this summer.
