The painting, which dates back to 1640, had been in a private collection for almost 400 years but has been sold and could be shipped overseas.
An export bar issued by the Government in November gives campaigners three months to save it. That expires in two weeks but can be extended for another five months.
The National Portrait Gallery and the Art Fund said they had received around £3.2m so far including £1m from the Sainsbury family's Monument Trust and £1m from members of the public.
The gallery's director, Sandy Nairne, said: "This is an incredibly generous response from the Monument Trust and from so many people across the country. Every pound really counts in helping to make it possible to keep this great painting on public view.
"The most common gift we have received from members of the public is £10, which goes to show that gifts in all amounts make a huge difference and continue to be vital in our efforts to save this outstanding self-portrait for the nation."
The painting, which is on show at the central London gallery, will go on a three-year tour if it is saved.