The sister of Kate Middleton is said to be in a relationship with the Made in Chelsea star's brother James, according to The Mirror.
The pair were seen having a dinner date at exclusive tennis centre Queen's Club in West Kensington, London.
They were also allegedly seen "openly flirting" with each other while enjoying a further date at Mayfair's Hakkasan restaurant.
A source stated: "Pippa and James sat in a secluded booth in the upstairs area, where it was quieter, sharing a bottle of white wine.
"They were deep in conversation and only had eyes for each other.
"Pippa was all smiles and kept giggling. They stayed for nearly three hours and didn't seem to want the meal to end."
Friends have also alleged that the couple have gone from "strength to strength" in recent weeks.
Pippa Middleton released her 'how-to-party' book Celebrate: A Year of British Festivities for Family and Friends in UK stores last week.
She made four outfit changes during the book's launch at Chelsea's Daunt Books store on Thursday (October 25).