The European Broadcasting Union (EBU), which organises the contest, has discreetly told Israeli officials that they were concerned over “politicisation” of the event.
Israel has the right to host the competition after Netta Barzilai won the 2018 contest in Lisbon last month.
Ms Regev has taken a lot of public criticism after last Saturday’s friendly match between Argentina and Israel’s national football teams was cancelled at the last minute, following a Palestinian campaign to oppose it.
The minister had insisted the game be moved to Jerusalem from the less controversial venue of Haifa for what her detractors said were political purposes.
She did not take part in the conference call Mr Netanyahu held with other ministers to discuss Eurovision.
Many in Likud said this was an intended snub of Ms Regev, who is a Netanyahu loyalist but was blamed by sources in his office for the match’s cancellation.
Mr Netanyahu said the government would not intervene on the host city decision and would leave it to Kan, the public broadcaster.
The corporation is expected to hold a tender in which other cities can bid. Tel Aviv, Haifa and Eilat have applied to host and, given the decision will be made in consultation with the EBU, Jerusalem is unlikely to be picked.