The Swede has been sidelined since suffering a serious knee ligament injury against Anderlecht in April but his recovery has since progressed more rapidly than expected, prompting Jose Mourinho to suggest the striker could be back before the end of the year.
The 36-year-old made an immediate impact in his first season in England, scoring 28 goals in 46 games in all competitions, but admitted the injury overshadowed what would have been an otherwise successful campaign, which saw United pick up three trophies.
"I said I have come back to finish what I started," Ibrahimovic said in an interview with Thierry Henry on Sky Sports.
"Everything I built up in the first season - obviously we won the three trophies - the ending for me was not the ending I wanted, or nobody wanted, especially after how the season went.
"The target is the Premier League. That is my target to finish. Everything I started in the first season, we will finish in the second one."
The former Sweden captain scored twice, including a late winner, as United beat Southampton in the League Cup final and had opened his campaign by scoring the winner in his side's 2-1 win over Leicester in the Community Shield.
However, he could only look on from the sidelines as his teammates went on to defeat Ajax, one of his former clubs, to clinch the Europa League and a first European trophy in nine years. Missing the final was a blow for Ibrahimovic, particularly as the final was held in Sweden, but he took recovering from injury as just another challenge.
"When it happened, it was easier for me to say that I would come back because then I had a challenge," he explained.
"The challenge was that I never had a major injury, and all these people talking that 'it's over' or 'he's too old', all these doubts that I had in my whole career.
"When that happens, it triggers me because it gives me energy and an objective. I'm challenging what I am able to do, how far I can take my body."
Earlier this week, his agent Mino Raiola revealed the Swede will play for a minimum of five or six more years at the least, a prospect which seemed highly unlikely when the striker underwent surgery following his injury.
However, Ibrahimovic echoed his agents' thoughts, insisting the injury will not dictate his future and that he was determined to leave football on his own terms.
"I will walk out just as I came in, I will not walk out limping.
"I will walk out the way I want to walk out. Even if I have to walk on water I will do that also."