Until the ugly aftermath of the death of Diana, Princess of Wales and her lover, Dodi Fayed, Harrods had been the proud holder of continuous royal warrants since 1913.
The bronze sculpture of the couple, who died in a vehicle crash in Paris two decades ago, has been on display at the west London department store since 2005.
Al-Fayed sold Harrods in 2010, and its new proprietors want to return the statue to the 88-year-old in an effort to gain back royal favor: the British monarchy has reportedly refused to shop there since Al-Fayed accused Prince Charles of being involved in Diana and Dodi's deaths.
Harrods is now owned by the Qatari royal family.
Mr Al Fayed said he wanted to keep the pair's "spirit alive" through the statue.
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The Queen had also dropped Harrods as her provider of Christmas puddings in favour of Tesco.
While the controversial statue remained in place, there had been little chance that Harrods would regain the favour of the British royals.
The news reports quoted Harrods managing director Michael Ward as saying that with a new Diana statue planned for Kensington Palace, it is the right time to return the one at the store to Al Fayed.
When the statue was unveiled, Fayed said it was a more "fitting tribute" to Diana than the official memorial fountain in Hyde Park that he described as a "sewer".
A spokesman for the Al Fayed family told The Times it was "grateful" to Qatar Holdings for preserving the memorial of the couple, adding: "It is now time to bring them home".