After a slow start to the season, Tottenham have kicked into gear and currently sit third in the table after a run of just one defeat in their last nine league matches.
Although Spurs will always struggle to compete with mega-rich City in the transfer market, Andre Villas-Boas appears to have forged a strong team spirit in the Tottenham camp and with the likes of Scott Parker and Benoit Assou-Ekotto returning from injury, the club look in little danger of falling away in the second half of the season as they did last term.
Tottenham trail last year's champions by six points with just under half of the season remaining and Dempsey is confident the Londoners can catch Roberto Mancini's expensively-assembled side.
"That's the goal," the Spurs forward said when asked if finishing second was a realistic target.
"Everybody wants to be pushing for great things and doing something special in their careers. We have the quality in our team and there's no reason why we shouldn't think that.
"We need to continue on this good run of form and get as many points as possible. You want to keep your feet on the ground and know there's a lot of hard work to put in if you want to accomplish your goals."
Like the team as a whole, Dempsey struggled at the start of the campaign, but he has found top form of late, scoring three times in his last two games. Two of those goals came on Saturday as Tottenham cruised into the fourth round of the FA Cup with an easy 3-0 win over League One side Coventry.
Dempsey, who missed two games over the festive period with a groin injury, is happy that he is back among the goals, but insists he can still do better.
"My season is going OK. I've got six goals and I think five assists in all competitions now, so it's starting to look better," Dempsey said.
"I'm someone who likes to score or get assists so it's good to be getting those stats up, contributing and trying to help this team do well. It's going well but I still want to be better at what I'm doing."