McKenna met the founder of Liverpool Football Club John Houlding, who invited him to Anfield to watch his Everton team play. He remained with Houlding after Everton left Anfield for Goodison Park. Houlding was a major driving force for Liverpool throughout the early years, and he used his connections to look for players in Glasgow. His team was known as the "Team of Macs" due to the number of players with "Mc" in their surname: Duncan McLean, James McBride, Malcolm McVean, Hugh McQueen, Matt McQueen, John McCartney, Bill McOwen and Joe McQue.