Gossip Cop search A Taylor Swift and Joe Alwyn in a rush to get married and start a family? That’s the story plenty of tabloids are pushing. Gossip Cop has investigated the claims and can set the record straight. Taylor Swift And Joe Alwyn ‘Rushing Down The Aisle’? Not long ago, the National Enquirer reported that Taylor Swift wanted to marry her boyfriend, Joe Alwyn, as soon as possible. The tabloid alleged that quarantine had only brought the couple closer together, and they were ready to walk down the aisle. An insider source explained to the magazine, “Taylor said no other man she’s ever dated comes close to Joe and doesn’t want to lose him,” and their Nashville elopement would come any day now.