The 28-year-old scored a close-range winner in United’s 2-1 Premier League victory on Sunday — his first goal since signing on a season-long loan from Monaco.
United will reportedly have to pay around £43 million ($68.7 million, 54.8 million euros) next year to make the move permanent, but Falcao says he already has designs on a long-term stay at Old Trafford.
“Me and my family are happy here, and we would like to stay for many years at Manchester United,” Falcao told the club’s in-house television channel, MUTV.
Falcao’s strike, after Angel di Maria’s first-half opener had been cancelled out by Steven Naismith, took United into the top four for the first time this season.
He also posted a picture on his Instagram account of him posing with team-mates inside the United changing room, accompanied by the caption: “Very happy with my first goal and win in @manchesterunited.”