Brand claims to have slept with more than 1000 women. Since the breakdown of his marriage in 2011 he has been linked with a string of women, including Geri Halliwell.
Khan, 39, former wife of cricketer turned politician Imran Khan, also had a relationship with actor Hugh Grant before they split in 2007.
Meanwhile, there is speculation Grant's other famous ex, Liz Hurley, has split with fiance Shane Warne after an unusual Twitter silence.
The pair, who frequently sent each other public tweets, haven't mentioned each other for several weeks, according to the Daily Mail.
Former cricketer Warne, who is in Australia, didn't mention Hurley when he celebrated his 44th birthday last Friday. He thanked his friends and family for birthday messages, but failed to mention the swimwear designer, who is back home in England.
The same day, Hurley tweeted that she spent the day fixing an alpaca fence at her Gloucestershire farm.
The couple were first linked in July 2010 after they were photographed chatting at the Glorious Goodwood Festival in Sussex.
Warne proposed to Hurley in October 2011 and in an interview last year, the couple spoke of their plans to marry this year, with ceremonies in Australia and England.