The previous Bush administration had pushed for the shield to protect against what it said was the possibility of Iran developing nuclear warheads to put on its long-range missiles. Russia sees the project as a direct threat to its own security.
"The meeting with [US Deputy Secretary of State] Ellen Tauscher and other US officials has just ended. A statement will be issued shortly," Polish Deputy Foreign Minister Andrzej Kremer told Reuters.
He declined to comment further. Earlier, before the talks at the Polish foreign ministry, Kremer said Warsaw saw a strong chance that the shield project might be halted.
"We know the review of the missile shield is not yet over and in 10 days Deputy Defence Minister Stanislaw Komorowski and I will go to Washington to find out. From different sources we hear there are serious chances the shield won't be deployed here," Kremer told Reuters.
Obama spoke by telephone with Czech Prime Minister Jan Fischer on Wednesday evening about missile defence, a spokesman for the premier said in Prague.
The Wall Street Journal, citing current and former US officials, reported on Thursday that Obama would halt the shield deployment because "Iran's long-range missile programme has not progressed as rapidly as previously estimated, reducing the threat to the continental US and major European capitals".
The Obama administration wants to "reset" battered ties with Russia so that the two former Cold War foes can cooperate on Iran, on fighting Taliban insurgents in Afghanistan and on reducing their vast arsenals of nuclear weapons.
Central European alarm
But Moscow's former satellite states in central and eastern Europe fear that any shelving of the missile defence shield project could mark a lessening of the US commitment to their security and could embolden an increasingly assertive Russia.
In an open letter to Obama in July, senior figures from the region including Václav Havel of the Czech Republic and Poland's Lech Wałęsa urged him not to be swayed by Russian objections in making his decision on the missile shield.
Poland and the Baltic republics, in particular, have been alarmed by what they see as Russian "neo-imperialism" in Moscow's dealings with ex-Soviet republics such as Georgia.
The deputy head of Poland's National Security Bureau, Witold Waszczykowski, told Reuters on Thursday the abandonment of the shield plan "would be very bad. Without the shield we would de facto be losing a strategic alliance with Washington".
For NATO member Poland, the timing of the report is particularly sensitive. Thursday marked the 70th anniversary of the Soviet invasion of eastern Poland following a pact between Moscow and Nazi Germany, an event seen by Poles as "a stab in the back". "I hope this is just a coincidence," said Waszczykowski.
(EurActiv with Reuters.)
