The singer, who turned on the lights at Westfield in Shepherd's Bush two years ago, will also perform a short concert for the 20,000 fans expected to attend.
"Rihanna's thrilled she has been asked again. She knows it's a big deal and is totally up for it - if it fits in with her schedule," a source told The Sun.
"Westfield have had a great year due to the Olympics and want to fork out to celebrate.
"Even though the final contract is still being thrashed out, they're prepared to pay up to £5 million for her. Organisers are expecting around 20,000 people to swamp the park.
"The Spice Girls were also discussed but Rihanna came out as the artist of choice."
Rihanna recently said that she doesn't like being "associated with anything that's untrue" in relation to rumours she was photographed taking cocaine.
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