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Trump is expected to issue more than 100 pardons and commutations on his last full day in office on Tuesday.
Two sources familiar with the discussions, who spoke on condition of anonymity, said Trump appeared to have been dissuaded from pardoning himself or members of his family.
Lil Wayne pleaded guilty last month to possessing a loaded, gold-plated handgun when his chartered jet landed in Miami in December 2019. He faces a sentence of up to 10 years in prison at a January 28 hearing in Miami.
Lil Wayne appeared to support Trump during last year's presidential campaign when he tweeted a photo of himself with the president and said he backed Trump's criminal justice reform programme and economic plan for African Americans.
The sources confirmed a New York Times report that the list of pardons and commutations is expected to include former New York Assembly speaker Sheldon Silver (76), who was convicted of corruption charges in 2015.
Trump's list is not expected to include Giuliani, the Trump private lawyer who has been a vocal proponent of the president's claims of voter fraud in the November 3 presidential election won by Democrat Joe Biden.
The sources also said not expected to get a pardon is Steve Bannon, who helped Trump win election in 2016 and was a senior White House adviser. Bannon (66) has pleaded not guilty to charges that he defrauded donors to "We Build the Wall," an online fundraising campaign that raised $US25 million ($NZ35 million).
Julian Assange, the Wikileaks founder, was also not expected to get a pardon, the sources said.
The US Justice Department in 2019 asked Britain to extradite Assange to the United States to face charges that he conspired to hack U.S. government computers and violated an espionage law.
A British judge ruled two weeks ago Assange should not be extradited to the US, saying his mental health problems meant he would be at risk of suicide.