The newly single 23-year-old country music singer desperately wants to date the hunky "Hangover" actor and has begged Lawrence, 22, to set them up, reported Radar online.
However, when Lawrence informed Cooper, 38, about Swift, he reportedly said he wasn't interested and that she was too young for him.
"Bradley has absolutely no intention of getting together with Taylor. First of all, her reputation precedes her. Bradley is very wary of dating someone who is a bit of a serial dater like Taylor," a source said.
"He thinks she is far too young for him and wants to date someone his own age, not 16-years younger because he is ready for something serious. It was a little awkward for Bradley. Jennifer came to him and told him that Taylor was interested in getting together," the source added.
"He had to politely decline, knowing full well that Jennifer and Taylor are friends. It was an ambitious move from Taylor, but she is going to have fixate on someone else as Bradley is just not that into her."
Swift has previously dated Joe Jonas, Taylor Lautner, John Mayer, Jake Gyllenhaal and Conor Kennedy.