The Sweden international has found the net seven times in nine Premier League appearances this season, putting him second in the scoring chart behind Erling Haaland, who has nine goals. He has also registered a goal and an assist in three Champions League outings.
That represents a significant improvement on his injury-disrupted first campaign at Anfield, when he managed only three league goals in 14 appearances, starting eight matches.
Speaking to Swedish journalists at the national team's training camp in Valencia, Isak was reluctant to suggest he had reached his best form.
“I have more to give,” he said.
The 27-year-old has also been assessing his contribution to Sweden, where he has often operated in a deeper position behind Viktor Gyökeres. That role has meant fewer opportunities to lead the attack himself, but Isak is comfortable adapting his game to the team's needs.
“I try to be flexible in my play. Of course, the role is different here compared with at my club. But it's also about getting the most out of the team. And it's about me being able to play and fulfil this role.”
Isak's international comments come after a contentious moment in Liverpool's 1-0 defeat by Arsenal on November 1. The forward was pulled by Jurrien Timber inside the penalty area as he tried to reach the ball, but referee and VAR decided against awarding a penalty.
The decision attracted criticism, with the Premier League's Key Match Incidents Panel subsequently judging that Liverpool should have been awarded a spot-kick.
Isak said he had not fully appreciated the extent of the contact while concentrating on getting to the ball.
“Now when I look back, it looks like a penalty, but it's not always easy when you're there on the pitch to understand exactly what is happening. I feel that I'm being pulled, but not that much. I was so focused on scoring,” he told Expressen.
He also rejected the suggestion that he should have exaggerated the contact to make the referee's decision easier.
“I don't think you need to exaggerate. But of course, if I had understood the situation better, I would have drawn the referee's attention to it more. It wasn't a case of being the good guy or not. I was trying to score.
“I'm a striker and I saw an opportunity to get to the ball, so I wanted to score.”
Liverpool manager Andoni Iraola has since indicated that he will encourage Isak to make more of such incidents in future, reigniting the debate over whether players who remain on their feet are disadvantaged when seeking decisions.
For Isak, however, the priority remains improving his own performances. His goals have helped Liverpool make a stronger start to the season, but he believes there is still room to become more influential for both club and country.