Former Bayern Munich coach Kovac was sacked on Thursday, but his dismissal has not yet been made official. According to sources, Clement has accepted a two-and-a-half year contract with the Principality side.
Clement, 47, has coached Club Brugge since May 2019 leading them to the last two Belgian league titles, with the club currently second in the table. The former Belgian international midfielder previously led Genk to the Belgian league title in 2019.
Kovac, 50, was told of the decision to terminate his contract which ran until 2023 by the club's board late on Thursday. The former Croatia international took over the under-performing French side from Robert Moreno in July 2020 on a three-year deal.
Monaco finished third last season but were eliminated in the Champions League's qualifiers and are sixth in the French table. There were reported tensions between Kovac and squad members including captain Wissam Ben Yedder.