The American needs to win three medals to surpass the overall record of 18, held by Soviet gymnast Larisa Latynina, but bombed out on his first race on Saturday when he finished fourth in the men's 400 individual medley.
The Americans are among the favorites for the men's relay although face a tough task winning gold against an Australian team that boasts the fastest two men in the world, including world champion James Magnusson.
The host-nation will get their opportunity to win their first medal in the pool when Rebecca Adlington defends her 400 freestyle title she won in Beijing, although she too faces stiff opposition for the gold.
The heats of both events will be held in the morning with the finals at night.
Sunday will also see the final of the men's 100 breaststroke and women's 100 butterfly with the fields already decided following Saturday's semi-finals.
Japan's Kosuke Kitajima has the opportunity to become the first male swimmer to win the same event at three Olympics when he booked his place in the breaststroke final.
Kitajima, who won the breaststroke double at Athens in 2004 and Beijing four years later, qualified sixth fastest overall with South Africa's Cameron van der Burgh setting the fastest time.
American Dana Vollmer cemented her place as the favorite to win the butterfly gold medal after setting the fastest time in Saturday's semi-finals.
The reigning world champion broke Inge de Bruijn's 12-year-old Olympic record in the heats then booked her place in the final when she stopped the clock at 56.36 seconds.
Australia's Alicia Coutts was second overall despite swimming just before the final of the 4x100m freestyle relay where she won gold.
Ryan Lochte and China's Sun Yang, who both won gold on Saturday, will be back in the pool for the heats of the 200 freestyle, which is looming as one of the best events of the swimming competition.
The pair are in the same heat in the lanes next to each other while world record holder Paul Biedermann and 400 silver medalist Park Tae-hwan are in other heats.
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