Henry began his two-month loan spell from New York Red Bulls in stunning fashion at the Emirates during the FA Cup third round tie and will once again be in contention for a place in the side when they face Swansea City at the weekend.
And with Arsenal currently trailing Chelsea in the race for the Champions League places, the Gunners' all-time record goalscorer wants to help push his side above their London rivals with the season now past the halfway mark.
"We obviously don't want to drop out of those positions," Henry told reporters.
"There's going to be a hell of a competition this year to be in them.
"But 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’s loan only runs until February 16 but that is now expected to be increased for a further 10 days, allowing him to take in the north London derby on the 25th.
The 34-year-old admitted the decision on how long he stays at the Emirates was not in his hands but added that he was determined to get the most out of his time at Arsenal before he has to return to New York.
"Remember I am a Red Bulls player, and all this depends upon what the boss decides to do, and how long I am going to stay," said Henry.
"But it would be a dream to be part of a team playing in the Champions League or playing against Tottenham. But that would be the same for any game, even if I never came on [from the bench]. I'm just trying to take all this in. That's something I didn't do enough when I was playing here before.
"When you're at the ground every three days, you don't enjoy it as you should. I know it's not going to last long. I guess it was always going to be surreal. I just hope I don't wake up tomorrow to be told by someone that this has all been a dream."
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