The 23-year-old midfielder joined Newcastle from Toulouse on a six-and-half-year deal and he insists the squad is strong enough to pull away from their precarious position in the table.
Alan Pardew's men have struggled badly this season after claiming a lofty fifth place in the previous campaign, but Sissoko feels the team has the potential to compete with the big guns in the top flight.
"My personal objectives really are to finish off this season as best as we possibly can. I am going to give everything I can so Newcastle finish as high up the league as possible," he said.
"For the future, I want Newcastle to be one of the very best teams in the Premier League. That's my wish and the club's also.
"I have signed here because I love the cub. They have some fantastic players.
"Newcastle aren't in the position where they should be at the moment, but I think if we all do well, we will finish as high as possible and really make the team one of the best in England."
The Magpies can ease their relegation fears with a win over Aston Villa on Tuesday and Sissoko is already aware of the importance of this fixture.
"Tuesday night will be a difficult night. Aston Villa are also in a pretty poor position at the moment in the league," he said.
"It's a match which we certainly can't afford to lose. We must make sure we are motivated for Tuesday night so we come away with a result."