The gallery, which is run as a charity, has been showing the painting since 2009 on loan from a private collection.
It now has the opportunity to buy the picture from the collector and is campaigning for funds. A gallery spokesperson said: “Now we need your help to ensure it can continue to be enjoyed by future generations.”
The artwork was originally owned by Frosca Munster, an ex-girlfriend of Wood. She bequeathed it to Winifred Nicholson, who had been a close friend and inspiration to the artist. Nicholson lived with the painting for the last years of her life.
Born in Liverpool, Wood (1901-30) became friends with experimental painter Ben Nicholson and Winifred, his wife. They painted landscapes and harbours and spent time in Cornwall together.
The gallery has already received nearly £200,000 in funding from the Art Fund, the V&A Museum and the Friends of Pallant House Gallery Acquisitions Fund. It needs another £15,000 to hit the target price of £212,333 and has a deadline of September 15.
Any funds raised beyond £15,000 will go towards the necessary conservation work on the picture.
The spokesperson said that everyone who has made a donation will be invited to a private reception at the gallery once the painting is successfully acquired.
To make a donation visit: https://platform.nationalfundingscheme.org/PHGC003?charity=PHGC003