Ladbrokes are offering odds of 1/5 on Caprice being evicted, with former 'Hollyoaks' and 'Holby City' actor Jeremy Edwards second favourite.
Ladbrokes spokesman Warren Lush said: "Caprice is the hottest eviction favourite so far this series and bookmakers are confident she'll be next out. Quite simply, we don't want to take much money on her as a shock looks very unlikely."
The 19-year-old rapper Kenzie, a member of the Blazin' Squad, saw his odds of winning the show slashed from 4/6 to 1/2.
"In recent hours, Kenzie has pulled even further into the lead," Lush said.
However, the race is far from over. Early favourite to win the show, former Happy Monday dancer Bez, is still in with a shout and could still defeat the rapper. Bez has already faced the public vote and survived.
Edwards and former Mrs Sylvester Stallone, Brigitte Nielsen, have little chance of winning. Nielsen's odds slipped to 3/1 from 2/1 as support for Bez grows.
Caprice will likely follow former Radio 1 DJ Lisa I'Anson out of the door. I'Anson was the third housemate to be voted out on Wednesday in a surprise eviction.
The housemates had been playing a game of hide-and-seek. I'Anson was in the diary room and told she would not be rejoining her fellow D-listers. On leaving the house, she said she was "glad to be out".
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