Israel does not want to build the Third Temple and actively
discourages Jewish activities on the Temple Mount. They do this
both because the official Rabbinical stance in Israel is that only
the Messiah can build the Third Temple and to avoid violence and
rioting from the Arab Muslim population which sees the Temple Mount
site as the third holiest site in Islam.
There are some Jews in Israel who want to build a Third Temple
to restore Judaism to the status it was 2000 years ago with animal
sacrifices and a closer relatonship to God. None of these groups,
though, has actual plans to rebuild the Third Temple; it's more
that they think about it on occasion. And they do not have the
endorsement of any serious or sizable Rabbinical authority.