Manchester United have won their last four league games on the trot and are now firmly placed inside the top four.
They are level on points with third-placed Newcastle, having played a game fewer, and are a point behind Manchester City, who are second, and will take on the reigning champions later this month.
The Red Devils are still looking to just finish inside the top four this season but Agbonlahor believes they should be seriously considering pushing for the Premier League title as well.
He insisted that Arsenal are likely to drop more points and he sees a way for Manchester United to get involved in the Premier League title race in the latter half of the season.
The former striker said on talkSPORT: “I said it last week that Manchester United should be looking at a title race.
“Everyone was like, ‘oh, you are crazy saying that’ but why not?
“A point behind Manchester City now, nine points behind Arsenal and Arsenal could drop points.
“Manchester United should be looking at pushing Arsenal.”
Manchester United’s next two league games are against Manchester City and Arsenal, and could be key in determining the extent of their ambitions this term.