It was claimed that chief executive David Abraham wrote to the glamour model in the wake of Ofcom's decision to uphold an official complaint by her solicitors regarding Boyle's disparaging comments about the 8-year-old, who suffers from numerous physical and mental conditions.
In the December episode, Boyle quipped: "Apparently Jordan and Peter Andre are fighting each other over custody of Harvey. Well eventually one of them will have to lose and have to keep him."
He later added: "I have a theory that Jordan married a cage fighter [Alex Reid, Price's second husband] because she needed someone strong enough to stop Harvey from f**king her."
Defended the network's decision to air Boyle's taunts, The Sun quotes Abraham as telling Price: "I appreciate the very personal perspective to your letter and I would like to reassure you that we never set out to offend or cause distress to your son.
"As we made clear in our submission to Ofcom, our detailed internal commissioning process meant that we were satisfied that you, and not your son, were the object of the satire."
However, Price's spokesperson denied that Abraham has apologised for the remarks. It has since been reported that the star has called for the firing of the chief executive.
Price's legal team previously described the comments as "discriminatory, offensive, demeaning and humiliating", while the reality star herself blasted Boyle's jokes and Channel 4's actions as "sickening".
Ofcom decided to uphold Price's complaint this week after determining that Boyle's comments were "highly offensive" and had a "straightforward focus" on Harvey and his disability.
The regulator received approximately 500 complaints about Tramadol Nights during its six-week run last year.
It was reported in January that Channel 4 will axe Boyle's series.