The Red Devils are the top scorers in the Premier League this season with 53 goals from 26 games.
But Ole Gunnar Solskjaer has failed to settle on a regular No 9, although Edinson Cavani has proven to be a hit since his free transfer after leaving Paris Saint-Germain.
But the Uruguayan, at 34 years of age, is not a long-term solution and Carragher believes an elite forward is needed to bridge the 12-point gap to leaders Manchester City and compete for their first title since 2013.
“I think Manchester United have a quality issue,” Carragher said on Sky Sports. “When the ball actually goes up to the front players, is there enough quality there? They are the top scorers in the Premier League, but have they got that player who can score goals in decisive games and take them to the league title?
“People talk about United needing a right winger, and they do, but they need a centre forward more. If United had [Marcus] Rashford on the left, a new centre-forward, and [Mason] Greenwood supplementing a new right winger, that would address the lack of quality.
“You look at the options. In this country it’s Harry Kane, or Erling Haaland who is coming through. You wonder whether they are players Manchester United should be targeting.”