The France captain has been put up for sale by PSG, according to media reports, after relations between the two parties soured last month.
Mbappe previously said he would not renew his contract, which expires at the end of next season, meaning he can leave for free in June 2024.
But PSG President Nasser Al-Khelaifi has said they will not let Mbappe, the French top-flight's highest scorer for the last five seasons, go for free.
"These players - all of them - must enjoy the same working conditions as the rest of the professional workforce," the
, the main trade union for professional football players in France, said in a lengthy statement on Saturday.
"The UNFP feels it would be useful to remind managers that putting pressure on an employee - via the deterioration of their working conditions, for example - to force them to leave or accept what the employer wants constitutes moral harassment, which French law firmly condemns.
"So, yes, the UNFP reserves the right to take civil and criminal action against any club that behaves in this way," the statement said.
PSG have won nine of the last 11 Ligue 1 titles, but their domestic success has not been matched in the Champions League - a trophy the Parisian club have never won despite all their investment in the squad.
PSG face the dilemma of allowing Mbappe to run down the final year of his contract and being unable to recoup any of the 180 million euros they spent in 2017 to sign him from AS Monaco.
Mbappe has been linked with a move to record 14-time European champions Real Madrid.
