Henry, who made his return to the North London club by scoring the winner against Leeds United on Monday evening, believes that Arsenal are slowly hitting top form.
The 34-year-old said: "I do think this team does have what it takes to finish in the top four, particularly if you think about the way the team has come back from the beginning of the season.
"I know that people want more, and I can assure you that the players want more. [Targeting a place in the top four is] not what you want to see as an Arsenal fan and, trust me, as an Arsenal player also. But the team is slowly getting into form. The season is still long, anything can happen."
Henry is currently at the Emirates on a short-term loan from New York Red Bulls and is expected to return to America in two months.