Both clubs were willing to trigger the midfielder's €60 million release clause, but Chelsea thought they had edged ahead of PSG by adding bonuses to make their bid more attractive.
However, sources have told ESPN that PSG made a new bid which is "significantly more" than Chelsea's highest offer, with the Premier League club not willing to pay a figure they now believe to be above the market rate.
Sources have also denied reports that Chelsea offered to buy a stake in Sporting as part of the agreement.
Ugarte had been willing to join Chelsea but PSG are now in pole position and are in the process of finalising personal terms.
The move comes as something of a blow to new Chelsea boss Mauricio Pochettino, who is said to be a big admirer of Ugarte.
But the club's decision also may also mark a slight change of approach in the market with Chelsea showing more discipline in their dealings after spending around £600m on 17 players in the first year of Todd Boehly and Clearlake Capital's ownership.