A source told the Daily Star newspaper: "Kate was so touched that Gaga sent her such a thoughtful present.
“Kate would have loved Gaga to be at the wedding, but because of her busy work schedule she can’t make it.
“But Gaga is hoping to stay with Kate at her Cotswolds home later this year."
Meanwhile, the 'Poker Face' singer is set to go on a five-day promotional tour of Taiwan from July 1-5, and Taichung city's government is so excited about the popstar's forthcoming visit they have branded July 3 'Lady Gaga Day', and will present the eccentric star with the keys to the city at a party to welcome her.
She will also play tracks from her latest album, 'Born This Way' at the event.
Taichung Mayor Jason Hu said: "We have spent a great deal of time and energy inviting Lady Gaga to visit Taichung and we are very pleased to see the success of our efforts.
"Therefore, we are determined to designate the day as 'Lady Gaga Day'.
“During the event, Lady Gaga might meet the media and I will represent our city in bestowing upon her the keys to the city."