According to The Sun, the pop superstar will spend time with Kinney and his family in Venice when she performs in Milan on the 'Born This Way Ball' tour.
"Lady GaGa has been talking non-stop of her passion for Venice and how romantic it is," a source told the newspaper.
"She is hoping to visit lots of churches with Taylor. When she does get married it will be in Italy. Some of her close friends and family are also hoping to fly over, so this could well be it."
GaGa was photographed in a wedding dress when spending the evening at London's Arts Club earlier this week.
The singer introduced Kinney to her parents in July, but has also dismissed rumours that she is engaged, adding that "music is my husband".
More recently, GaGa said that "divorce is not an option" for her, adding: "I'm going to get married and that's it, he's stuck with me. I want to find a man that feels the same."
Watch Lady GaGa marry Taylor Kinney in the 'Yoü and I' fashion video below:
Lady GaGa's 'Born This Way Ball' in pictures: