Milan have a two-point advantage on Inter and are the nominal hosts at the San Siro ground the two sides share.
They also won there earlier in the season but Inter have closed a gap that once stood at 13 points in mid-December and have by far the better form since the turn of the year.
"Maybe we're seen as favourites because of recent results, we've made a historic comeback and we don't want to stop there," said the Serbia captain.
"We won't let up, that's for sure, but I am a little worried about their professional pride.
"They will want to show they haven't spent 20 weeks leading Serie A for nothing, to show that they have quality."
Milan coach Massimiliano Allegri previously said Inter have more to lose in this game but it is the nerazzurri who are still in the Champions League and also have the Italian Cup to play for.
Milan's interest in the European competition is over for another season and the club's hierarchy surely would not be satisfied with merely a Cup victory for their year's efforts not to mention their economic outlay over the past 12 months.
Inter follow up Saturday's game with a clash against Schalke 04 in the Champions League on Tuesday but Stankovic doesn't believe that will be a distraction.
"We'll give everything against Milan and then we'll be taken by another emotion," he said.
"We know that the better you do at the beginning the better things happen thereafter.
"The Champions League gives you fuel for the league and vice versa.
"It's no coincidence that Milan dropped points against Bari and Palermo after going out of the Champions League."
Milan looked almost home and dry a couple of weeks ago after Inter had drawn away to lowly Brescia.
The rossoneri could have moved seven points ahead of their rivals with a victory but instead they drew at home to rock-bottom Bari and then lost away to Palermo the next week.
That has left them just two points above their bitter city rivals and under pressure also from Napoli, three points back, and outsiders Udinese, six points behind.
For Inter coach Leonardo it may be a strange feeling as he takes charge of his third derby, but first on the nerazzurro bench.
Last season he had an awful record in these two games, losing 4-0 when Gennaro Gattuso was sent-off and then being beaten 2-0 in the second match despite Inter finishing the game with nine men.
However, that was only his first season as a coach and Stankovic believes the Brazilian, who only joined Inter in late December, has come on in leaps and bounds since then.
"(The 4-0) defeat was only his second match on the bench, it could have been that he didn't have everything under control," said the 32-year-old.
"Since then he's taken stock and improved. We had a mission (when Leonardo arrived) which was to rein in Milan so we could be playing for something important come the derby.
"With Leo we've done something incredible."
