Ki joined the Swans from Celtic for £5.5million in the summer to replace Allen, who joined the Reds for £15m.
The two men could line up against each other in Sunday's Premier League clash at Anfield but the South Korean believes it is not a personal duel as they are very different players.
"Joe is a good player and hopefully I can show I'm a good player too," said Ki. "I watched him many times when he was at Swansea and I played against him in the Olympics too. He can pass, he can do the defensive work very well and he just knows how to play football.
"Sometimes people expect me to be better than Joe was when he was here. But I respect him too much to think like that. He is a good player in his own right with great qualities.
"We are different kind of players. I am obviously bigger than him and we have different aspects to our game, but we are also similar in our way of thinking about the game and wanting to pass the ball."
Ki has been asked to play various roles by Michael Laudrup but does not see it as an issue, saying: "It is true my role varies a lot but it is not difficult. I think I know how to play in whichever type of midfield role I have.
"All the midfielders at Swansea know what we want to do in games and our roles so we can change. It is not tough to change roles. We are comfortable both defensively and offensively and that is what helps us."
The Swansea players have enjoyed warm-weather training in Dubai this week ahead of the Capital One Cup final against Bradford later this month, but Ki is not looking past Sunday's clash at Anfield.
"It was good to go to Dubai. It's nice to have some good weather, even though it was not that hot," he added. "It was a perfect environment for us to train and also get some rest before two big games. But we cannot think about the final when there is Liverpool to play first.
"The next game is always the most important one especially when you are going to Anfield. We beat them in the cup and it would be great to get one over on them in the league.
"We want to keep the confidence and good atmosphere in the squad before the final, and the best way to do that is to perform well and hopefully get a result."