The Liberal Democrat leader is at odds with Edinburgh-born Tory Mr Gove after it emerged he is to insist teachers should be qualified and the national curriculum should be taught in every school.
It appears to put him at odds with the Coalition policy on free schools.
Mr Clegg said his intervention was only a "perfectly sincere difference of opinion". He said he supported free schools, but that as more of them decided to run themselves he had to ask if they had "certain basic quality standards so that parents... can be assured that their children are going to be taught by qualified teachers, are going to be taught the national curriculum."
Downing Street expressed surprise at Mr Clegg's comments. A Department for Education spokesman said free schools were raising standards and giving more choice.