Plans to collect data from schools on teenage pregnancy, obesity and drug abuse could be ditched in favour of schools conducting their own pupil and parent surveys.
Ministers said this week that they would consider a self-evaluation approach in light of fears that schools could be ranked in league tables according to pupil wellbeing issues they could control.
Ministers also revealed they were interested in the balance scorecard approach to school accountability, which is being touted as a fairer alternative to league tables.
The news came at a Labour party conference fringe meeting after teachers' leaders criticised the wellbeing plans.
Chris Keates, NASUWT general secretary, warned that issues such as the quality of relationships were important to pupil wellbeing but intangible and "difficult to quantify in terms of crude indicators".
Jim Knight, the schools minister, said he would work with unions to see if schools could carry out their own satisfaction polls.
"A measurement of satisfaction in the service, and (pupils' and parents') satisfaction in respect of wellbeing, are really interesting areas we should be exploring," he said.
Mr Knight also revealed that he had been to Alberta, Canada, to look at the scorecards used there for school accountability.
The TES revealed this month that Downing Street advisers were enthusiastic about a similar scheme in New York that grades schools, taking into account pupil background, attendance and parents' opinions alongside raw exam results.