Milan finished third last season but were a massive 15 points behind champions Juventus, with Napoli spitting the two giants of Italian football.
The Rossoneri made a dreadful start to the season and only a superb late surge saw them secure a place in the Champions League.
But it is getting back to the summit of the Italian game that all at the club crave as they look to regain the title that they last won in the 2010-2011 campaign.
Coach Massimiliano Allegri is currently looking at a few new players but finances are tight and he has made it clear that a couple of stars might have to leave before any reinforcements arrive.
But Zapata is convinced that, if they can hit the ground running, the San Siro outfit already have enough talent in the ranks to challenge for league honours.
"We have to immediately begin well," he told Sky Sport Italia. "The aim is to improve next season and we are all working hard for that.
"More reinforcements? This team is already very strong as it is, we will be fighting for the Scudetto."