The 42-year-old daytime TV presenter has received coaching from Peter Wilson, who won gold in the double trap at London 2012, and is now eyeing up a spot at the Rio Games after being told she has "a natural gift" for shooting.
"The feeling when you hit the clays is amazing," Sykes told The Sun. "It's cool. When I really like something and get into it I get quite obsessed with it. I get addicted to things and would put in the time.
"I'd love to be able to compete in Rio in 2016. Who says you can't have a go at making it to the Olympics?"
Sykes and Wilson first got in contact on Twitter and a training session was arranged after they met in person at The Sun's Military Awards.
"If she put in the work she could make Rio," Wilson claimed.
Bookmakers Paddy Power have already given relatively short odds of 25/1 that Sykes will represent Great Britain at a Rio 2016 shooting event, and 50/1 that she will win gold.
Sykes hit headlines last year after exchanging racy tweets with 26-year-old lover Jack Cockings, to whom she is now engaged.
"A lot has been made of Jack's age, but I always go for younger men," she said in an interview last year.
"I'm very silly and you don't tend to meet that many 40-year-old men who want to lark around."
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