The gallery said it had been involved in discussions about acquiring some items from her wardrobe.
But it said it only collected items of "outstanding aesthetic or technical quality" and no formal offer was made.
More than 300 items will now be sold at auction next month instead. Lady Thatcher died two and a half years ago.
She was the longest-serving premier of the 20th Century and Britain's only female prime minister to date.
The clothes to be auctioned by Christie's include her blue velvet wedding dress and various power suits worn during her tenure in Downing Street, plus handbags and jewellery.
A spokesperson for the museum told The Daily Telegraph: "The V&A politely declined the offer of Baroness Thatcher's clothes, feeling that these records of Britain's political history were best suited to another collection which would focus on their intrinsic social historical value.
"The museum is responsible for chronicling fashionable dress and its collecting policy tends to focus on acquiring examples of outstanding aesthetic or technical quality."
The museum later issued a further statement saying: "Several years ago, a general discussion took place to explore whether some pieces from the wardrobe of Baroness Thatcher might be added to the V&A's collection.
"These conversations did not develop. The V&A would like to make it clear that no formal offer was made for the museum to acquire the collection.
Business Secretary Sajid Javid tweeted: "Shame the V&A has turned down Thatcher's personal collection. I for one would have loved to see it!"
In recent years the museum, which described itself as "the world's leading museum of art and design", has put on crowd-pleasing shows of fashion by designer Alexander McQueen and clothes worn by pop legend David Bowie.
The Victoria and Albert Museum in London has turned down the chance to exhibit former Prime Minister Margaret Thatcher's clothes.