Police are investigating Derek Curran, 53, after he was suspended from his current school - Castlebrae Community High in Edinburgh – over allegations of sexual misconduct.
But according to the Edinburgh News, the police inquiry is expected to focus on his time in charge at another school in the city, Forrester High, where he worked for six years.
Mr Curran has not been charged with any offence and the pupil who made the complaint is understood not to have attended either school.
The paper reports that the woman told officers she became pregnant during a relationship spanning several years - and alleged that a later paternity test showed Mr Curran was the father.
Now in her 20s, it is thought she gave birth after her 18th birthday.
The allegations against Mr Curran only came to light as a result of a separate police inquiry.
A source told the paper: "The student says she fell pregnant during their relationship, which lasted a number of years since she was at school, and she became pregnant. She's had a paternity test and it confirmed Curran was the father."
A Police Scotland spokeswoman confirmed the force had launched an inquiry which was at an 'early stage' but was unable to comment further.
The development has sparked shock among parents. Susan Heron, vice-chairwoman of Castlebrae High parent council, said: "It's an absolute mess. I think the department have took the right action by removing these people while the investigation is done.
"We had a meeting with the new headteacher and concluded that what's important is that the school continues to run.
"Hopefully this mess that's unfolding will be taken away from the school, because it's really nothing to do with the actual school. Let's get on and finish the school year."
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