Germany international winger Sam, 26, joined Schalke at the end of 2013-14 season after signing a pre-contract agreement in January - ending his four-year association with Leverkusen.
Sam's new employers - Schalke - finished third behind champions Bayern Munich and Borussia Dortmund in the Bundesliga last season, while they reached the last 16 in the UEFA Champions League.
And Sam, who scored in Schalke's 5-0 win over DJK TuS Hordel in their pre-season opener on June 5, is hoping to achieve that feat again.
"I've settled in well and definitely want to achieve great things here," Sam told Bundesliga.com.
"We want to finish in the top three and get at least as far in the UEFA Champions League as we did last season.
"If Bayern or Dortmund slip up, we want to take advantage."
Jens Keller's men kick-off their Bundesliga campaign against Hannover 96 at HDI-Arena on August 23.
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