The four figurines will cost £5m to secure for the V&A's permanent collection, with half the money still to be raised.
Historical novelist Hilary Mantel called the pieces a connection to "one of our liveliest eras of history".
Cardinal Wolsey was the hugely influential advisor to King Henry VIII.
He appears in Mantel's Booker-winning novel Wolf Hall.
The bronze figures, designed to adorn the corner of Wolsey's tomb, were sold during the English Civil War, separated and eventually lost. His tomb was never completed.
The pieces emerged in recent sales and have been brought together at the V&A for the duration of the museum's campaign to secure them.
They have announced that the National Heritage Memorial Fund has granted £2 million towards the purchase price, with the Art Fund giving an additional £500,000.
The public is being asked to donate to the campaign online or via text, or in the gallery.
V&A director Martin Roth called the angels "a vital part of our national history and artistic heritage" and intends them to be purchased by the museum to be "held and preserved" there for future generations.
The two pairs of figurines were commissioned in 1524 from Florentine sculptor Benedetto da Rovezzano as part of a grand tomb reflecting Wolsey's stature and importance.
The cardinal, who eventually died in 1530, spent the last years of his life at odds with Henry VIII, after he failed to secure a Papal annulment for his marriage to Catherine of Aragon.
Henry VIII intended to use the tomb himself, but work was slow and it was not finished in time for his death in 1547.
The angels disappeared from view until 1994, when two of them appeared at a sale but were not catalogued as the Wolsey bronzes.
The Victoria and Albert Museum has launched a campaign to acquire a set of bronze angels intended for Cardinal Wolsey's tomb.