Having gone through 10 different coaches in the last seven years, success-starved Schalke have had little to celebrate since their 2011 German Cup triumph and Champions League semi-final run.
Tedesco arrived with little fanfare, the Italy-born 32-year-old's experience limited to youth teams and a few months at a second division club.
But the Bundesliga rookie appears to have settled into the role after an uncertain start, with Germany internationals Max Meyer and top scorer Leon Goretzka leading his team.
Both, hugely talented players, are set for offers from big clubs at the end of the season but their current coach is determined to give them plenty of reasons to stay.
"I do not think that we are without a chance (in keeping them)," Tedesco said. "We have a lot to offer. Schalke is a great club."
Schalke started the season with three defeats in their first six matches but have since turned a corner, winning three of their last four to climb to fourth, level on 20 points with bitter rivals Borussia Dortmund, whom they play next weekend.
Their playing style may not be the most spectacular but his team have conceded just one goal in their last four league games.
"Defence in football is extremely important," Tedesco said. "If we concede few goals then we are also very hard to beat."
Hamburg, former European and German champions, look set for another nail-biting campaign, battling relegation as they have done almost perpetually in the past five seasons.
They lost seven and drew one game before beating VfB Stuttgart in their previous match to climb out of the relegation spots and up to 15th place.
Champions Bayern Munich, unbeaten in Germany and Europe since Jupp Heynckes replaced Carlo Ancelotti last month, host Augsburg and will be looking to protect their four-point lead over second-placed RB Leipzig, who travel to Bayer Leverkusen.
Dortmund, without a win in their last four matches, face VfB Stuttgart on Friday ahead of next week's Ruhr valley derby.
(Reporting by Karolos Grohmann; Editing by John O'Brien)
