Schools in Hampshire are among those who have been advised to extend the £60 fixed penalties to also include lateness.
The Sunday Times reported that some councils had advised schools to give out the penalty notices if children are often late to class.
Hampshire County Council issued its latest guidance in 2015, helping to make sure schools have a consistent approach to periods of unauthorised absence.
Councillor Peter Edgar, the council’s executive member for education, said: ‘We work closely with our schools, and in partnership with families, to prioritise good attendance to ensure all our children achieve the best education they can, and the results are that attendance is higher than the national average.
‘Occasionally, a fixed penalty notice to parents for persistent pupil lateness may be issued, if a pupil has been late on at least ten occasions, and this has been recorded as an unauthorised absence.
‘However, fines are not automatically issued at this stage.’
He added that the decision to issue a fine would be up to the school, and would only be used when other strategies, such as a formal warning, had been used.
Hampshire County Council oversee all schools in Hampshire, except in Southampton and Portsmouth, where schools are advised by the city council.
Tom Bennett, the government’s behaviour tsar, said sanctions such as litter collection or the removal of chewing gum could be imposed on pupils, with the fines being a last resort.
He suggested adults walk with their children in the mornings, adding: ‘Most pupils would rather lose an arm than be seen walking up to school with their parents.’
A Department for Education spokeswoman said: ‘Pupils being punctual to lessons not only benefits their learning but also helps them develop core skills which will stand them in good stead for future employment.
‘It is right that schools monitor patterns of lateness and address it where it becomes a concern.
‘It is a matter for individual schools to decide when to close their register and take action as needed, provided it is in line with the local authority’s code of conduct.’
Portsmouth City Council has been approached for comment.