Biden will announce the news in his State of the Union address, a source said.
Russian forces are continuing their attempted push through Ukraine from multiple directions, while Ukrainians, led by President Volodymr Zelenskyy, are putting up "stiff resistance," according to U.S. officials.
The attack began Feb. 24 as Russian President Vladimir Putin announced a "special military operation."
Russians moving from Belarus towards Ukraine's capital, Kyiv, don't appear to have advanced closer towards the city since coming within about 20 miles, although smaller advanced groups have been fighting gun battles with Ukrainian forces inside the capital since at least Friday.
Russia has been met by sanctions from the U.S., Canada and countries throughout Europe, targeting Russia's economy and Putin himself.
In another indication that an invasion of Ukraine may be very close to taking place, Russian military leaders have gone to their command center, and cyberattacks are underway, according to a U.S. official.
Gen. Mark Milley, chairman of the Joint Chiefs of Staff, believes any invasion has to happen during the night, the official said.
-ABC News’ Chief Global Affairs Correspondent Martha Raddatz
The U.N. Security Council will meet in another late-night session at 9:30 p.m. ET, a U.N. diplomat told ABC News.
Ukraine’s foreign minister Dmytro Kuleba called for the meeting earlier Wednesday evening.
-ABC News' Conor Finnegan
Ukrainian President Volodymyr Zelenskyy gave an impassioned televised address, in which he said Ukraine doesn’t want war and rejected Russia’s claims that Ukraine is a threat or home to Nazism.
Zelenskyy said he tried to call Russian President Vladimir Putin on Wednesday. “The result -- silence,” he said.
Zelenskyy spoke in Russian for part of the address to appeal directly to the Russian people.
“We don’t need war. Not a cold one, nor a hot one, nor a hybrid one,” Zelenskyy said.
“We are separated by more than 2,000 kilometers of shared border. Along it today stand your troops, almost 200,000 soldiers, thousands of military vehicles,” he added. “Your leadership has approved their step forward, onto the territory of another country. And this step can become the start of a big war on the European continent," he said.
-ABC News' Patrick Reevell
A no fly notice was issued for an airport in Kharkiv, a city in eastern Ukraine only 20 miles from Russia.
The Notice to Air Mission (NOTAM) will close the airport until 8:30 a.m. Thursday.
The move comes after the Ukrainian military told leaders that Russia may target Kharkiv in an attack, according to sources.
Satellite imagery shows Russian troop deployments less than 50 miles from the city.
-ABC News' Kirit Radia
