The 20-year-old Wales midfielder took counsel from the former Scotland captain, currently the technical director at Old Trafford, before undertaking the third loan spell of his career after time spent at Charlton and Croatian club Istra 1961.
Ahead of the trip to St Mirren in the cinch Premiership on Saturday, Levitt said: "Darren Fletcher spoke to me a few times before I came up and he said, 'Go and show what you can do, it's a good league, the quality is very good and it is very physical and try to do well'. He is very supportive.
"I was with them in pre-season for a month or so and he was always on to me, wanting the best out of me, day-in, day-out in training. He was always helping me if I was struggling, always by my side in training really. If I needed anything I asked him and he was always there.
"It is always good to get out on loan to get game time, to try to improve yourself as a player.
"Hopefully I can show what I can do here and show the players and staff what I am capable of.
"United just wanted me to go out and express myself and obviously they will assess me when I go back but they just want me to do my best."
Levitt impressed in the league win over St Johnstone and the defeat against Hearts before playing for Wales in their goalless friendly in Finland during the international break.