The young couple, who announced in April they had split, attended a party at an army barracks together earlier this month, newspapers claimed in their Sunday editions.
William, 25, has also invited Middleton to attend a memorial concert to his late mother, Princess Diana, to be held at London's Wembley Stadium next Sunday, the Mail on Sunday reported.
A spokeswoman for William's Clarence House office declined to comment on the reports.
"We don't discuss William's private life, it's a matter for him," she said, on customary condition of anonymity, in line with policy.
Britain's News of The World tabloid claimed the couple had been on a string of low key dates since their April split.
William, second in line to the British throne and a second lieutenant in the country's army, celebrated his 25th birthday Thursday and gained access to part of the inheritance left him by his mother.