The American model is the latest celebrity to sign up for the diving reality series, according to The Sun.
However, Bourrett is allegedly concerned that her large breasts may make diving difficult.
"She is concerned hitting the water during a dive will hurt, as if you do have large boobs it can be quite painful," a source said.
"The coaches have promised to teach her the right techniques to make sure she experiences as little discomfort as possible."
Olympic medallist Daley will train a number of celebrities to dive efficiently in the programme, to be hosted by Vernon Kay and Gabby Logan.
Eddie 'The Eagle' Edwards is also said to have joined the lineup, alongside Joey Essex and Katie Price's ex-partner Leandro Penna.
The new series will launch in early 2013 on ITV1.