Johns secured the portrait at Artcurial’s March 27 sale in Paris at a hammer price of €49,000 (£42,155) or €63,700 including buyer’s premium.
The gallery will now research the portrait, in enamel on copper, and compare it with a version in the Ashmolean Museum in Oxford. There is also a pastel on paper of the same sitter at the V&A.
Johns said: “We look forward to comparing the Ashmolean version, which is signed on the reverse, and it is my opinion that our piece was probably made and kept by the artist. There are very few enamel/miniatures by this great Swiss artist, the finest being a self-portrait in the Royal Collection.”
He has a buyer in mind.
Fawkener (1694-1758) was a merchant and diplomat and a friend of philosopher Voltaire who he met in Paris on his way home from Aleppo in 1725.
Voltaire dedicated his tragedy Zaire to Fawkener in 1733.
Johns has sold a number of works by Liotard. Last year German private museum Karlsruhe Museum paid €1.4m (£1.2m) for a Liotard portrait of Mme Paul Girardot de Vermenoux from the gallery.