Maybe the Getty, since they finally got their hands on Turner's Modern Rome last year?  And they have been spending vast amounts of cash on acquisitions of late.

Modern Rome was their second painting by Turner of course, the other being the ex-Holloway College Van Tromp; and they have two watercolours.  But nothing by Constable as yet so this is their only opportunity to get a really important one.  I doubt somehow that his last great six-footer, still in private hands, would be allowed out of the country.

Fortunately, the portrait of Henry VIII is owned by the Spanish State, and like all works of art from national museums,is inalienable, in contrast to Constable's 'Lock' which is owned by the Baroness and only was on loan to the Thyssen museum with the rest of the Carmen Thyssen collection, but the collection of her husband, With Van Eyck, Duccio, Caravaggio, Carpaccio, Weyden, Bacon, etc is owned by the Spanish.