The former Barcelona captain has established himself as first-choice right-back even though he is known to prefer a central defensive role.
Liverpool have a £47 million option to secure Araujo's services on a full-time basis, although whether the six-time European champions will want to spend that sum on a player who turns 28 in March remains to be seen.
"It's very early to talk about these things," the Uruguayan international said ahead of Tuesday's Champions League match at home to Villarreal.
"I'm really happy to be here, my family are also very happy but it's a bit early to be talking about these things."
Araujo, who has played 10 times for Liverpool, is already popular with fans and appears to have adjusted quickly to the demands of the Premier League.
"Coming to Liverpool, it's not easy," he said. "There are those demands, that responsibility. Personally I'd already experienced that in Barcelona.
"It depends on the personality of each player and how they (face) that challenge. I knew it was a new challenge coming to the Premier League but from the first moment I arrived I had no doubts I had to give everything here. And that's how I live it.
"It's not easy to be in big sides, but that's what we came to do. That's the work we have to do."
Andoni Iraola's Liverpool are fifth in the league phase of the Champions League with two wins in two games, against Atletico Madrid and LASK.