De Boer replaced Sam Allardyce as head coach of the Eagles this summer, and he got his first taste of winning with the London club in last week's EFL Cup fixture with Ipswich Town at Selhurst Park, which ended in a 2-1 home success.
Palace have lost each of their three Premier League matches at the start of the 2017-18 campaign, however, the latest of which was a 2-0 home defeat to Swansea City at the weekend.
A record of zero goals scored and six conceded has led to early criticism of De Boer, and according to The Guardian, the Palace hierarchy are 'deeply unimpressed' with the start to the season.
The report adds that Palace are becoming 'increasingly unconvinced' that the Dutchman is capable of turning things around, which could see the 47-year-old become the first Premier League manager of the season to be sacked.
Former Ajax boss De Boer, who was sacked just 14 games into his tenure with Inter Milan last year, was heavily critical of his players following the loss to Swansea on Saturday afternoon.