Fallon will pitch against Berlin Cameron United, Crispin Porter & Bogusky and 180, Bravia's US agency of record. A decision is expected next month.
Sony is understood to be seeking an agency to create a global campaign to drive sales outside Europe, although it is thought that the decision whether or not to run the advertising would be left up to individual regions.
Fallon has held the European advertising account since 2002, but many of its spots, including "balls", "paint" and "Play-Doh", have also run in the US.
All three ads have won awards at Cannes, most recently "Play-Doh", which was awarded a gold Lion at this year's festival in June.