The 19-year-old midfielder has featured for the French giants eight times but with three years remaining on his deal is looking to leave in search of regular first-team football.
According to Sky Sports, the Scottish champions are preparing a £2million offer for Michut.
Earlier this year, it was reported in France that having been left out of a run-of-the-mill league fixture of no importance towards the end of the season convinced the player that his future lay elsewhere.
Spanish side Sevilla were one of the clubs touted as a possible destination for Michut and L’Equipe reported PSG would be looking for €8million for a talent who has been a regular for France Under-19s.
Celtic have had previous joy in unearthing talent without a future at PSG, signing Odsonne Edouard before selling him to Crystal Palace for a profit.