Israel's Haaretz newspaper reported that France was also considering withdrawing its envoy, and the two countries were coordinating discussions over a number of punitive steps.
Both embassies declined to comment on the reports, but the British issued a statement saying they had made clear they would not support strong Israeli retaliation to a UN vote last week that gave the Palestinians de facto recognition of statehood.
"The recent Israeli government decision to build 3,000 new housing units threatens the two-state solution and makes progress through negotiations harder to achieve," the British embassy in Tel Aviv said.
"We have called on the Israeli government to reconsider."
A diplomatic source, who declined to be named, said London would decide later in the day whether to recall its ambassador.
Such a move by both London and Paris would represent a severe diplomatic reproach to Netanyahu. Israel's Vice Prime Minister Moshe Yaalon told Israeli Army Radio he was not aware of any recall.
"I did not hear of this, either via the foreign ministry or the prime minister's office. Therefore I have a hard time believing it is true," he said.
France's foreign ministry played down the report. "There are other ways in which we can express our disapproval," a foreign ministry official told Reuters.
Netanyahu has brushed off world condemnation of his latest settlement plans, which were announced on Friday just hours after the United Nations voted overwhelming to upgrade the Palestinians' diplomatic status.
"We will carry on building in Jerusalem and in all the places that are on the map of Israel's strategic interests," Netanyahu said on Sunday at a weekly cabinet meeting.
Besides authorizing 3,000 new homes in and around Jerusalem, the Israeli government also agreed to expedite planning work for thousands more homes on land near Jerusalem that critics say would kill off Palestinian hopes of creating a viable state.
In another blow to the Palestinian Authority in the West Bank, Israel announced on Sunday it was withholding Palestinian tax revenues this month worth about $100 million.
Israel said it was taking the money to help cover a Palestinian debt of $200 million with the Israeli Electric Corporation.
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