If Kyiv does not call elections, the US is threatening to withdraw promised security guarantees, the newspaper's sources say.
The report follows increased pressure to end the war by the summer.
They want everything ready by June, President Volodymyr Zelenskyy said last week.
He then referred to the White House's desire to change focus ahead of the fall midterm elections in the United States.
The Americans have bought the Russian argument that Ukraine must hold presidential elections, says Jakob Hedenskog, an analyst at the Center for East European Studies at the Swedish Institute for International Affairs.
"This is a way for Russia to weaken Ukraine and the Europeans," says Hedenskog, "and he believes that US President Donald Trump sees Ukraine as an obstacle to his goal of entering into lucrative agreements with Russia and appearing as the great peacemaker."
Many obstacles
Hedenskog says that Russia has exploited the ongoing negotiations with Ukraine and the US to increase its attacks and try to force a capitulation from Ukraine. Russia would like to see an election and hopes for a more compromise-minded or pro-Russian candidate - an opportunity that Hedenskog considers to have been lost since the invasion.
Obstacles include ensuring the safety of candidates, voters and election workers, the mobility of international election observers, and voting opportunities for soldiers at the front and for internally displaced persons. It is also difficult to maintain information security when Ukraine is exposed to daily information and cyber attacks from Russia.
In addition to the security aspect, the constitution and emergency laws prohibit elections during a state of emergency.
"If you start changing them, you risk ending up in a legalistic quagmire," says Hedenskog.
"They do it once, and then several times, and in the end there is no constitution left."
Great pressure on the people
Jakob Hedenskog believes a referendum on a peace treaty also complicates the issue of making concessions in territories that Russia wants to control.
"If Ukraine is pressured into making territorial concessions in order to get security guarantees and is otherwise handed over entirely to Russia, there is enormous pressure on the Ukrainian leadership, but also on those who vote. If they say no, the entire existence of Ukraine is called into question. Is it reasonable to put it to a referendum?"
The details of plans for elections and referendums have not been officially confirmed.
