Hazel O'Neill, from Cotswold Archaeology, who is leading the project, said: "We've been going for about a month and we've found some really lovely things."
If the target was not met, the sculpture by the Wakefield-born artist would go to a private buyer and be taken overseas.The appeal is backed by artists and creatives including Sir Antony Gormley, Anish Kapoor, Jonathan Anderson, Richard Deacon, Katy Hessel, Veronica Ryan, Joanna Scanlan and Dame Rachel Whiteread.
The piece is one of only a handful of wooden carvings made by the artist during the 1940s, when she lived in St Ives, Cornwall, with her young family.If bought, the Hepworth said it would be a "star piece" in its collection.The gallery also planned to lend it to other museums and galleries across the UK, "opening up access for people everywhere".
Simon Wallis, gallery director, said: "We established The Hepworth Wakefield 14 years ago to celebrate, explore and build on Barbara Hepworth's legacy."This sculpture is the missing piece, a masterpiece which deserves to be on display in the town where Hepworth was born."
Sir Antony said: "Barbara Hepworth's work remains a luminary example of both an engagement with modernism and a return to direct carving.
"The opportunity for the museum named after her to acquire this important work is precious and should be supported."The portrait was made when Gandhi went to London in 1931 for the second Round Table conference, held to discuss constitutional reforms for India and address its demands for self-governance.
It will be auctioned in the second week of July at Bonhams."This is a painting of unique historic and cultural significance. It would be great if it could be seen and appreciated more widely, whether in India or elsewhere," Caspar Leighton, a great nephew of the artist, told the BBC.
According to Bonhams, Clare Leighton "was one of the very few artists admitted to his office and was given the opportunity to sit with on multiple occasions to sketch and paint his likeness".The works remained in the artist's collection until her death in 1989 in the US, after which it was passed down through her family.