The 23-year-old centre-back joined the Premier League outfit from Paris Saint-Germain on a long-term contract on Monday.
"My aim while I am here is to play in the Champions League with Liverpool," he told Liverpool's official website. "I remember their teams when they were in the competition when I was younger.
"The Champions League is a tournament that all the great clubs in Europe participate in and that's where we need to get to.
"With the team we have, and the means put at the disposal of the players, the technical support and the whole club and its supporters are in a good position to get there. This is our objective."
Sakho has played 14 times for the France national team.