"Antoine was informed he was being sacked today by Leonardo," the source said, adding that the manager's assistants were also being fired.
Kombouaré, who took over as coach of the Paris club in May 2009, moving over from Valenciennes to replace Paul le Guen, has already told certain close friends that he had lost his job, the source said.
PSG later Thursday issued a statement appearing to confirm the development.
"Paris Saint Germain and their manager Antoine Kombouaré clarify that they are calmly holding talks which will be concluded shortly and which will enable each side to preserve their own interests".
His sacking comes the day after PSG moved back to the top of the French first division with a 1-0 win at St Etienne in the last round of matches before the winter break.
Despite the good form in the league, the explosive Kombouaré's position had been under threat for several weeks with Leonardo holding talks with Italian coach Carlo Ancelotti, who has been out of work since being fired by Chelsea.
Others mentioned as possible replacements were Dutchman Frank Rijkaard and former PSG midfielder Claude Makelele.
A former popular player with the club, Kombouaré enjoyed mixed success in his first two seasons as coach placing fourth in the league last year and reaching the final of the French Cup where they lost to league champions Lille.
But the parameters and expectations all changed in the close-season when the club was bought by wealthy investors Qatar Sports Investments (QSI).
The Gulf company strode into the French capital with a 70 percent controlling stake and their president Nasser Al-Khelaifi promised "to make the club a great team and a strong brand on the international scene."
They promptly spent €85 million ($111 million) in the summer to attract new talent including a massive €42 million forked out to Italian side Napoli for 22-year-old midfielder Javier Pastore.
In recent weeks Leonardo has been in talks to bring England star David Beckham to play in Paris for a huge salary although there has yet to be an official announcement on his arrival.
PSG meanwhile crashed out of the French League Cup and the Europa League and struggled for league points in November before rediscovering their form in the last fortnight.
Several sources told AFP that there were also concerns among the club's Qatari owners over what they saw as the conservative style of play preferred by Kombouaré at PSG and whether or not he would be able to handle some of the big signings that had come his way.
Born on the south-west Pacific island of New Caledonia, Kombouaré established a reputation as a rugged centre-back in a 15-year playing career with Nantes, PSG, Swiss side FC Sion and Scottish club Aberdeen.
Having earned his coaching spurs in charge of PSG's reserves, he spent a little over a year at Strasbourg before moving to Valenciennes (VA), whom he led to the Ligue 2 title in 2006 in his first season in charge.
At Valenciennes his outbursts at referees frequently landed him in hot water with the football authorities but he succeeded in establishing VA in the elite before returning to the Parc des Princes in 2009.