Walter Mazzarri's men have put their poor run of form behind them and now sit one point adrift of fourth-placed Fiorentina having gone five matches unbeaten.
And Hernanes, who made the switch from Lazio in January, feels a club of Inter's stature can feel confident of achieving their goal at the end of the season.
"The Inter shirt is a powerful one," Football Italia quote him as telling Corriere dello Sport. "This is a serious and important club.
"In terms of quality, I think we're nearly on par with (champions and runaway leaders) Juventus. In my life, I've always believed that you can do a lot despite having little - but here we have a lot, so I'm sure we can win.
"I came here to win and that's what I want to do. In the next two or three years I want to lift the Scudetto with Inter."
And the Brazilian revealed former club Lazio's failure to break into the Italian elite had become a point of frustration before his departure.
"Teams that aren't Milan or Inter or Juventus can't fight for the title, and that annoyed me at Lazio," he added.
"I have some wonderful memories of Lazio, but I'm an Inter player now.
"I believe fourth place is still possible. Fiorentina have the Europa League to think about, but we can just concentrate on the league."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
