The homes would be built in 20 settlements and outposts, the Peace Now campaign group reported.
A tender was put out for a further 651 homes.
There was no confirmation of the reports from Israel’s Defence Ministry.
On Tuesday, Defence Minister Avigdor Lieberman announced his intention to approve the construction of 1,285 settlements and said he would push forward planning for 2,500 more.
Lieberman said the 1,285 should be built in 2018.
The construction of Jewish settlements on the West Bank is one of the most contentious issues in the decades-long and bloody dispute between the Israelis and the Palestinians.