The Sun newspaper cited an unidentified royal source as saying the couple were "closer than ever."
"Only after they took a step back did William and Kate have space to examine how they really felt," the source was quoted as saying.
Middleton on Sunday attended a concert celebrating the life of William's mother, Princess Diana, further fueling rumors that the couple have reconciled. William's Clarence House office has declined to comment on media reports that the two are back together.
William, who is second in line to the throne, broke up with Middleton in April as speculation swirled that the two were about to marry. Middleton had been pursued by photographers outside her London home and nightclubs in scenes that drew comparisons to the coverage of Diana.
"William has persuaded Kate that the problems of dating a future king are a price worth paying," the source was quoted as saying.
The report prompted bookmaker Ladbrokes to announce it would no longer take bets on who William will marry. After their split, bookies initially put the odds on the couple marrying at 16/1, but the odds eventually improved to a 1/3 chance as more gamblers put their money on Middleton.
"We thought the pair had split for good," Ladbrokes spokesman Nick Weinberg said, adding the public "clearly had more faith than the bookies."
The armored train with North Korean leader Kim Jong-un arrived at the railway station in Vladivostok at around 11 o'clock in the morning of April 24
In 1994, a former employee of the State of Arkansas filed a sexual harassment lawsuit against Democratic President Bill Clinton
The submarine will be the first carrier of Russia's new ominous weapon - the Poseidon underwater drone