Klaas-Jan Huntelaar has not given up hope of winning the Bundesliga during his time at Schalke.
Last month, Huntelaar, 31, prolonged his stay with the Royal Blues until 2017.
When his contract ends the Netherlands international will have been at the club for seven years, and he is hopeful of lifting some silverware before then.
Schalke won their last major trophy -- the DFB-Pokal -- in 2011, but have not won the league title in nearly 57 years and never in the Bundesliga.
"There were enquiries from the Premier League and from Ajax for instance, but we have super fans here and a great stadium," Huntelaar told kicker. "Schalke are a super club and I can achieve my goals here."
When kicker asked the striker whether leaving the Royal Blues might have been the better option if he wants to win titles, Huntelaar replied: "No. I have won the cup with Schalke in 2011, but I also talk about the championship.
"I would not write that off for all time. Bayern probably will win seven to eight titles within a decade, that's clear. But when they are not on top, when they falter, we should be there. Schalke's goal has to be to compete for the title."
Huntelaar urged Schalke to at least challenge the current German champions and said his club "can't make do with the fact that Bayern are always number one."
This season, however, Schalke already seem out of the title race as they trail league leaders Bayern by 18 points.
Schalke sit fifth in the standings, but are only one point behind third-placed Bayer Leverkusen, who sit in the position that guarantees direct Champions League qualification in the Bundesliga.
"Personally, I would not be satisfied with anything but at least finishing third, maybe even second," Huntelaar said. "It's my fifth season at Schalke now, and we have been very consistent in the past. I've played in the Champions League four times, and once in Europa League. We want to continue that run."