The Evening Standard newspaper reported that organised gangs had offered a year in wages to call centre staff in return for access to UK credit card details.
And US credit card giant Capital One pulled out of India after unauthorised credit levels were offered by call centres.
MEPs are tabling a motion on Monday at the Employment and Social Affairs Committee calling for an investigation into the issue.
Bill Miller, MEP for Scotland, who is backing the motion, says action needs to be taken before attempts to get credit card details become more widespread.
"It is a worrying consequence of the trend towards outsourcing," he said.