The ex-couple were angered by a controversial gag on Boyle's Channel 4 show Tramadol Nights about Price's son Harvey - who is practically blind and suffers from a number of disabilities.
On Tuesday night's programme, Boyle said: "Jordan and Peter Andre are still fighting each other over custody of Harvey - eventually one of them will lose and have to keep him."
He went on to say: "I have a theory about the reason Jordan married a cage fighter - she needed a man strong enough to stop Harvey from f**king her."
According to the Daily Star, Price said: "Harvey Price is a little miracle. Every day he overcomes so many difficulties and has so many battles to win due to his medical problems. I love him and am deeply proud to be his mother.
"If Mr Boyle had a tenth of his courage and decency, he would know that to suggest, let alone think funny, that Harvey may sexually attack me is vile and deeply unfair. Mr Boyle clearly has serious issues and those that give him a TV platform to say such disgusting things need to look at themselves very honestly."
Confirming that her lawyers are investigating the matter, Price added: "To bully this unbelievably brave child is despicable; to broadcast it is to show a complete and utter lack of judgement. I have asked my lawyers to write to Channel 4."
Andre's representative also said: "We're all disgusted by these comments. Peter is angry and very upset at Harvey being mocked in this way. Children, especially a disabled youngster, should be off-limits."
A spokesperson for Channel 4 defended the joke, saying: "People know what to expect with Frankie. We make it very clear about what type of content his show contains."
Boyle has frequently been criticised for his controversial material, which has previously included gags about Soham murderer Ian Huntley, the Palestinian crisis, Down's Syndrome sufferers and Cumbria killer Derrick Bird.