Lazio finished ninth in the Italian top flight last term, meaning they will not compete continentally this season.
However, following the arrivals of the likes of Stefan de Vrij, Filip Djordjevic and Marco Parolo, Klose - who won the World Cup with Germany last month - feels the Rome club can challenge for the top six.
"We have two competitions, the league and the Coppa Italia," said the striker. "It will be important for us.
"We will play only on the Sunday, so during the week we will work hard. I am happy with the new coach, whilst many new players have arrived. Hopefully we will be good.
"I like this Lazio, now we have to continue to work together. It is important. When I arrived, the club bought six players and the squad moved forward well. Hopefully the same can happen this year.
"Will we be the surprise of the season? I do not know, we will have to prove it on the field. We have trained well, we have to show everything on the Sunday.
"The two Milan teams, Juventus and Roma are ahead of us.
"We will see how they do, their shape. Playing every three days is not easy. But I think only of Lazio."
Lazio's begin their Serie A season with a trip to Milan on August 31.
