The PM's gift list includes a handbag by Gerald and Sue Bodmer, who make bags for The Queen, government papers show.
There is also a "silver item" from ex-New York mayor Michael Bloomberg and three pairs of shoes.
Mrs May decided not to buy any of them - under the rules she has to pay for any gift worth more than Â£140.
She did, however, decide to hand over Â£225 for clothing from Lady Jubie Wigan, who set up the Sugarplum Children charity for youngsters with diabetes, and Â£244 for jewellery from Nadja Swarovski.
The transparency records cover October to December - but it was a similar story during her first months in Downing Street, although she did purchase some tights from upmarket hosiery brand Luxury Legs and a scarf from Mayfair fashion house Halcyon Days.
Unclaimed gifts to the PM remain in the government departments to which they were given.
For the three months to December, these include hampers from the ambassador of Saudi Arabia and the Sultan of Brunei, "wine and dates" from the president of Algeria and a fan from entrepreneur Sir James Dyson.
The documents also detail Mrs May's Downing Street meetings, including a chat with former Labour PM Tony Blair, on November 26, to discuss his former role as a Middle East envoy.
Mrs May also had a meeting with former US secretary of state Henry Kissinger in October for a "general discussion".
A series of newspaper editors and television political editors, including the BBC's Laura Kuenssberg and Andrew Neil, also had meetings with the PM.
Daily Mail editor Paul Dacre had dinner at No 10 but no-one was invited to Chequers, the prime minister's weekend retreat, over the period.
The records also confirm Mrs May's meeting with Nissan on 14 October.
The car manufacturer announced it was investing in production of new Qashqai and X-Trail models at Sunderland after receiving government assurances that EU withdrawal would not affect the plant's competitiveness.
She also discussed Brexit, human trafficking and homelessness with the Moderator of the Church of Scotland - and met the Archbishop of Canterbury to talk about education, counter-terrorism, modern slavery and foreign affairs.
She is known for her love of shoes and high fashion - but Theresa May has not been tempted by many of the items given to her since moving into No 10.