The Art Fund, which oversees art purchases for the nation, said the government's National Heritage Memorial Fund had provided 750,000 pounds (US$1.3 million; 1.1 million euros) toward the purchase price of 1.4 million pounds (US$2.5 million; 2 million euros), the AP reports.
An additional 116,000 pounds (US$208,000; 174,000 euros) still needs to be found to ensure the gallery acquires the painting from the estate of Lord Lothian, who died last year.
The painting shows Donne, who lived from 1572 to 1631, at around the time he wrote what is considered to be one of his greatest poems, "To His Mistress Going To Bed," from the highly charged and often erotic Elegies series.
Other best-known lines include "No man is an island, entire of itself" and "Send not to know for whom the bell tolls, it tolls for thee."
The painting of the poet and dean of
It was bequeathed to an ancestor of Lord Lothian in Donne's will and has remained in the family for four centuries.
The National Portrait Gallery plans to put it on permanent display alongside pictures of other famous Britons including William Shakespeare, Ben Jonson and Michael Drayton.
Outgoing US President Donald Trump does not accept the outcome of the November election. Trump has also refused to attend Joe Biden's inauguration ceremony on January 20