The Red Devils have won four and drawn one of Carrick’s five games since he was appointed head coach until the end of the season after taking over from Ruben Amorim.
Carrick is a fan favourite to take the role full time at the end of the season and if he secures Champions League football, he will likely be head and shoulders above every other candidate.
United go to Everton this week knowing victory will put them clear in fourth and just three points adrift of third-placed Aston Villa.
However, speaking to OLBG, Heskey believes that Carrick has a long way to go and must still prove his worth to get the role.
“Have we seen enough to think there’s longevity for United in this form under Carrick? Not really. I think it’s just short-term but again, you never know what it comes to that long-term.
“At that point it becomes a question of what the future looks like within the actual playing staff as well. Players need to go. Who comes in? Is he astute enough to know where to make those changes and who is going to be the next player to slot in?
“United have a whole department for that, but he’s got to play a part in it as well because you can’t just throw players at a manager and tell him to work with them.
“You've got to know what you want. What does it look like? What’s the formation? What does the club want? What do they want going forward? Even just where do you want us to finish? Things like that, so everyone's held accountable.
“You've got to remember, this new era of coaching and management, it's not the manager who builds the team anymore. He's going to have a little bit of a say but everyone says this manager brought in this player but no. Sometimes they never bring these players in.”
Champions League qualification has become more of an expectation rather than a hope under Carrick and if secured, Carrick could be handed the job almost immediately after the season ends.