The moves are part of a broader effort by NATO to strengthen the alliance’s air, sea and land presence in Eastern Europe in response to Russia’s new assertiveness in the region.
It is not yet clear what additional troop deployments the United States and other NATO nations might undertake in Eastern Europe after the exercises and to what extent the moves would ease anxieties there.
The land-force exercises the Obama administration is planning are extremely modest.
The exercise in Poland, which is expected to be announced next week, would involve a United States Army company and would last about two weeks, officials said. A company consists of about 150 soldiers.
The exercise in Estonia would be similar, said a Western official who declined to be identified because he was talking about internal planning.
Although the exercises would be short, the United States is considering other ways to maintain a regular ground-force presence in Eastern Europe by rotating troops and conducting training there.
“There’s an entire range of possibilities and measures that are being considered,” Defense Secretary Chuck Hagel said on Thursday in a joint news conference with Poland’s defense minister, Tomasz Siemoniak. “Rotational basis of training and exercises are always part of that.”
The company-size Army exercise that is planned is far from the sort of NATO deployment that Poland’s foreign minister, Radoslaw Sikorski, suggested this month when he told reporters that he wanted the alliance to deploy two combat brigades with as many as 5,000 troops each in Poland.
This week, NATO’s top military commander, Gen. Philip M. Breedlove, gave members of the alliance a range of options for strengthening its military posture in response to Russia’s annexation of Crimea, along with his own recommendations.
The measures include immediate, midterm and long-term steps. One option, General Breedlove said in an interview this month, is to move the 4,500-member American combat brigade from Fort Hood, Tex., to Europe. But Obama administration officials have not publicly supported such a step.
The first hint that the Obama administration plans to announce that American troops would be sent to Poland was provided on Friday by The Washington Post, which noted that Mr. Siemoniak had said that the move had been agreed to on a political level but provided no details.
The United States has already sent 12 F-16 fighter jets and 200 support personnel to Poland.
NATO’s secretary general, Anders Fogh Rasmussen, said this week that the alliance would fly more air patrols over the Baltic region and that allied ships would deploy to the Baltic Sea.
Mr. Rasmussen left open the possibility for additional deployments, including on land.
“More will follow, if needed, in the weeks and months to come,” he said.