Changes to the GCSE religious studies curriculum due to come into effect next September mean that schools will have to teach a second faith as part of the course.
The reform was brought in by Education Secretary Nicky Morgan following concerns over the Trojan Horse scandal in Birmingham, which saw fundamentalist Islam taught in some of the city's schools. It means that at least 25 per cent of the course will have to be devoted to another religion as well as the student's own faith.
Mirvis opposed the change at the time, saying in a statement that while he supported efforts to inculcate repect for other faiths, "forced changes to the Religious Studies GCSE, used as a primary tool for so many to learn about their own faith, is not the right way to achieve these shared goals".
However, according to the Jewish Chronicle, he has now said that teaching Islam will give children the opportunity to learn about a "poorly understood" religion.
A spokesman for Rabbi Mirvis said: "Losing 25 per cent of the time allotted for teaching Jewish studies as part of the religious studies GCSE was a serious loss for Jewish education in our schools."
But he added: "It is more important than ever that our children have a better understanding of Islam and that we build strong relationships with British Muslims.
"As such, the Chief Rabbi has recommended that schools take this opportunity to teach students Islam, a faith which is widely discussed but often poorly understood in public discourse."
He said that Mirvis had not issued any formal guidance on the issue as it was for the schools to decide for themselves, but he had had "positive discussions" with several schools.
About 60 percent of school-age Jewish children attend Jewish schools.