The paper reports that the singer has come under "intense pressure from fans" to cancel the June 2018 gig, "especially in her home country of New Zealand".
Last night, Lorde replied to fans on Twitter, revealing that she had been consulting with "many people" about the topic, and is "considering all options", adding: "Thank u for educating me i am learning all the time too".
Her tweet came in response to an open letter by New Zealanders Nadia Abu-Shanab and Justine Sachs, who urged Lorde to show solidarity with the Palestinians' anti-apartheid struggle.
Today, millions of people stand opposed to the Israeli government's policies of oppression, ethnic cleansing, human rights violations, occupation and apartheid
"As part of this struggle, we believe that an economic, intellectual and artistic boycott is an effective way of speaking out against these crimes. This worked very effectively against apartheid in South Africa, and we hope it can work again."
Lorde announce her tour dates on 18 December, prompting criticism from a number of fans about the scheduled Tel Aviv performance.
The Boycott, Divestment and Sanctions (BDS) campaign has attracted the support of a number of artists and cultural workers, including Roger Waters, Brian Eno, Ken Loach and Arundhati Roy.
Omar Barghouti, co-founder of the BDS, said: "Inspired by the cultural boycott of apartheid South Africa, BDS expects and appeals to conscientious artists to refrain from performing in Israel or participating in events that are sponsored by Israel or by entities that are complicit in Israel's egregious human rights violations until it meets its obligations under international law."