The photogenic 24-year-old equine physiotherapist first drew attention by visiting jewelry shops in December with Mike Tindall, a rugby ace on England's national team. The couple met in Australia following England's 2003 World Cup victory.
Then on New Year's Eve, Phillips was photographed wearing a ring on her left ring finger, the newspaper said.
The flurry of bets rang alarm bells at the William Hill bookie agency.
"We are going to be cautious and close the betting before we get stung," a spokesman said.
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