The 21-year-old striker is currently enjoying a spell of playing regular football with the Bundesliga outfit, having failed to establish himself at Old Trafford.
Red Devils boss Sir Alex Ferguson is blessed with arguably the greatest forward options English football has ever seen, with Wayne Rooney, Robin van Persie, Javier Hernandez and Danny Welbeck all currently vying for first-team inclusion.
That competition for places has limited Macheda's development at Manchester United, prompting him to seek loan spells away from the club, with stints at Sampdoria, Queens Park Rangers and now Stuttgart.
The Italian arrived at the Mercedes-Benz Arena in the January transfer window, and the German club are understood to have an option to buy him permanently this summer.
"My experience at Stuttgart is going very well," Macheda told calciomercato.it. "I have immediately familiarised myself, and the relationship with my team-mates and coaches is great.
"In June the loan will end but I already have a verbal agreement with Stuttgart to extend my stay. If there is a chance to, I would be really happy to stay."
Macheda hasn't ruled out the possibility of returning to England one day, but also revealed a desire to test himself in Serie 'A', back in his native Italy.
"My relationship with Sir Alex Ferguson is great and it's clear that I have always had the desire to return and play for the Red Devils.
"But returning now would not be good for my career because I need to play with continuity."
He added: "In the future I would like to go back to my country, and play in Serie A."