Trump, however, is still deciding on a variety of options being presented to him by U.S. military leaders, senior administration officials told NBC News.
The Washington Post first reported that the plan could involve an increase of at least 3,000 troops, with the U.S. asking other NATO nations to match. The U.S.'s force in Afghanistan currently totals about 8,400.
More from NBC News:
South Koreans elect new leader after ouster of Park Geun-hye
Jakarta governor 'Ahok' jailed for blasphemy over viral video
Sally Yates, acting Attorney General fired by Trump, testifies on Flynn saga
A U.S. official told The Post that Trump wants to "start winning" again and has the backing of top Cabinet officials. He is expected to make his mind up on strategy before attending a May 25 NATO summit in Brussels, the newspaper reported.
One senior administration source told NBC News a decision would happen "soon."
But former Secretary of State Condoleezza Rice said Tuesday that the president will need to better explain his strategy in a country that remains mired in conflict for over 15 years.
"What is the strategy now?" Rice said on TODAY. "It doesn't make sense to increase troop strength to keep doing the same thing."
Among the possibilities that are being mulled over: allowing Defense Secretary James Mattis to set the troop levels for Afghanistan — similar to the Pentagon doing so for Iraq and Syria, sending potentially several thousand more troops there, and ending some Obama-era rules on how the U.S. military operates in the country, including on its ability to go after the Taliban.
Discussion surrounding how to handle Afghanistan comes just weeks after the U.S. dropped the largest non-nuclear weapon ever used — also known as the "mother of all bombs" — to obliterate an ISIS tunnel complex in eastern Afghanistan. Two U.S. Army Rangers were also killed last month in the same region during a firefight outside of an ISIS compound.
Coalition forces have been engaged in a dual conflict against both the Taliban, which was toppled in 2001, as well as ISIS's regional branch for South Asia known as ISIS-K.
Gen. John Nicholson, the top U.S. commander in Afghanistan, has suggested to Congress that the NATO coalition needs several thousand more troops in the country. He has also not refuted previous reports that Russia is helping to arm the Afghan Taliban.
Trump held a different view on Afghanistan before he entered politics, tweeting in 2013 that the U.S. should leave immediately or "if we have to go back in, we go in hard & quick."
Rice, who was also national security adviser under President George W. Bush, didn't specifically say whether she believes additional troop deployment would do the trick this time around — particularly after the Obama administration's surge that saw 100,000 troops there in 2010 failed to suppress the Taliban."
"Well, I'd certainly urge the President to look at how we can turn the tide in Afghanistan," she told TODAY. "I know we've been there a very, very long time and obviously the goal is to have a government that's stable in Kabul that can't be assaulted by the Taliban."
While the U.S. may find Russian diplomacy helpful for dealing with North Korea, Rice cautioned about trusting President Vladimir Putin when it comes to Middle East policy.
"One of the first conversations needs to be with Vladimir Putin and to say, 'Do you really want to get back into Afghanistan after what happened to you before in Afghanistan?' There's no reason for the Russians to be arming the Taliban," Rice added, "and so that conversation needs to take place."