Mark Hughes' troops have lived up to ambition, fuelled by owner Sheikh Mansour's finances, and sit fourth in the table after drawing with Aston Villa on Monday.
City also have a game in hand over Chelsea, Manchester United and Tottenham and Given wants to take advantage.
He said in the Manchester Evening News: "The next couple of games we are aiming for maximum points, and we still have a game in hand on the teams around us. We are looking to get as close as we can.
"It was important not to lose at Villa, because now we can look forward to the next game and hopefully push on up the league."
However, Given, who will be in World Cup qualifying action for the Republic of Ireland this weekend, knows there is still a long way to go in the season.
He added: "Nothing is handed out in October - all the prizes are handed out in May, and it will be a long winter. But we hope to be still up there in spring."