The Ashmolean has raised £860,000 to acquire J M W Turner's The High Street, Oxford but hopes the public will help contribute towards the final £60,000.
On loan from a private collection since 1997, it has been offered to the nation in lieu of £3.5m inheritance tax.
Director Dr Alexander Sturgis described it as the "greatest painting of the city that has ever been made".
He added: "The importance of keeping this beautiful painting in Oxford cannot be overstated.
"High Street, Oxford is the young Turner's most significant townscape... if the Ashmolean does not acquire the painting, it will be sold on the open market.
"All major oil paintings by Turner that have been offered at auction in recent years have been bought by foreign buyers."
Turner created the painting of one of Oxford's most picturesque streets in 1810 after being commissioned by Oxford printseller James Wyatt for 100 guineas.
He painted more than 30 watercolours of Oxford in his lifetime, and is credited with inventing new techniques in landscape painting, such as making skies and clouds look luminous and expressive.
The museum has received a £550,000 grant from the Heritage Lottery Fund (HLF) towards the painting, as well as £220,000 from the Art Fund, and £30,000 from the Friends and Patrons of the Ashmolean.
Stuart McLeod, head of HLF South East England, said it would be "unthinkable" if it did not remain on public display in Oxford.
Stephen Deuchar, director of the Art Fund, said: "This most important picture simply must be saved by the Ashmolean."
A previous campaign by the museum in 2012 was successful in keeping Edouard Manet's portrait of Mademoiselle Claus in the UK.

Gul, 32, has not played for his country at one-day level since April 2015.
Pakistan face two ODIs against Ireland in Dublin, on 18 and 20 August, before a five-match series against England, starting in Southampton on 24 August.
Opening batsman Sami Aslam, 20, who scored two half centuries in the third Test against England last week, received his first call-up.
Paceman Hasan Ali, 22, is the other new face in the squad.
Gul, who has taken 173 wickets in 126 ODIs, played in Pakistan's World T20 warm-up games in early 2016, but failed to make the final squad.
Pakistan ODI squad: Azhar Ali (capt), Sharjeel Khan, Sami Aslam, Mohammad Hafeez, Babar Azam, Shoaib Malik, Sarfraz Ahmad, Mohammad Rizwan, Mohammad Amir, Wahab Riaz, Hasan Ali, Umar Gul, Imad Wasim, Yasir Shah, Mohammad Nawaz.
A museum has launched a fundraising campaign to keep the "greatest" ever painting of Oxford on show in the city.
[NEXT_CONCEPT]
Pakistan have recalled fast bowler Umar Gul for their one-day international series against England and Ireland.