The scheme, put forward by the Tate in partnership with the National Portrait Gallery, had hoped to bag £10 million from the Heritage Lottery Fund, but the application was turned down late last month.
Carole Souter, director of the Heritage Lottery Fund, said: ‘This decision was not taken lightly. We thought that Tate’s proposals were excellent, with a particularly strong emphasis on skills and conservation training.
‘However, this was a competitive round of funding – nearly five times over-subscribed – and we had to make some tough decisions on the day.’
The building had been earmarked for the car park of Mandela Way, adjacent to Tate’s collection store.
It is believed that Tate is still committed to building the scheme, despite missing out on the lottery funding.