The 18-year-old has two relay titles and golds in 200 freestyle and 100 backstroke already this week and if she manages a fifth triumph she would match a feat achieved only by American Tracy Caulkins and Australian Libby Trickett.
Franklin, who is also due to represent her nation in Sunday's 4x100 medley relay, suffered her first setback of the championships when she was fourth in Friday's 100 freestyle having won all four of her previous finals.
"I really hope to medal in the 200 back and our team has a really good chance in the relay on Sunday," she said after the 100 freestyle.
There are four other finals on Saturday.
Franklin's compatriot Katie Ledecky can win her fourth title of the week in the 800 metres freestyle after golds in the 4x200 freestyle relay and the 400 and 1,500 freestyle, when she smashed the world record.
If she wins as expected, Ledecky will be the second woman to claim the 400, 800 and 1,500 golds in the same championships after Hannah Stockbauer of Germany in 2003.
Florent Manaudou of France looked in top form as fastest qualifier for the 50 freestyle, while Jeanette Ottesen Gray was quickest in the women's 50 butterfly semi-finals.
Ryan Lochte can add his fourth gold this week with victory in the 100 butterfly, with South African Chad le Clos also strongly fancied.
(Reporting by Iain Rogers, editing by Ken Ferris)
