Bates is hoping the clash, to be played over the weekend of January 8/9, will be chosen as one of four ties scheduled to be screened live on TV.
He told Yorkshire Radio: "I'm sure Liverpool against Man U will be one of the choices but there are four games so there's a reasonable chance, which would be great because it would be seen around the world.
"It'd be of great benefit to our many fans abroad and for people around the world to see how Leeds United are getting on."
Leeds famously knocked out Manchester United at the same stage of last year's competition at Old Trafford before taking Tottenham to a replay in the fourth round and Bates added: "We're delighted. We wanted another big game and this is another test of our progress. It'll be tremendous. There'll be 60,000 in a fantastic stadium and it'll be a test of how much progress we've made."