Athletics has been the subject of allegations of widespread doping, with the likes of Italy and France having already criminalised the use of prohibited substances.
"It is an interesting idea," Crouch told the BBC.
"I've asked officials in my department to have a look at the issue."
She added: "We will make a judgement based on that in the near future."
Crouch said in August that current sanctions were tough enough for Britain not to have to criminalise doping.
The new world anti-doping code, which came into effect from 1 January 2015, means offenders now miss at least one Olympic Games.
