The X Factor contestant pursued the glamour model-turned-bodybuilder following her guest appearance in the reality show earlier this year.
However, 19-year-old Cocozza - who recently claimed to have sex four times a week - revealed that Marsh was resisting his advances.
"I texted Jodie to ask her out. I f**king love her," he told The Sun. "But she's having none of it. Anyway, she couldn't handle me."
Cocozza went on to detail the kind of girl he would like to settle down with - once he sleeps with 100 women.
"I want a girlfriend, yeah," he said. "But she needs to be small with dyed red hair, piercings, tattoos and be Scouse."
Cocozza is said to be working on a reality show with fellow Celebrity Big Brother housemate Kirk Norcross, which will apparently "be all about [them] getting p*ssed and pulling fit birds".
> Frankie Cocozza flees female admirer with passport - pictures