The 35-year-old recently took charge of the League One side following the sacking of David Weir.
Despite guiding the Blades to only their second win of the season against Port Vale on Saturday, Morgan insists that he does not want to be appointed United's permanent boss.
"The club's been working very hard behind the scenes, but I'm not interested in wanting the job long-term," he told Sky Sports News.
"I've already spoken to the chairman and I will get behind the new manger when the time comes.
"While we're in charge, my job is to get the players more confident to kick on."
Former Derby County manager Nigel Clough remains the favourite to take over at Bramall Lane.