Nani's agent, Jorge Mendes, has spoken to United's executive vice-chairman Ed Woodward about the possibility.
And he has also discussed the future of another of his clients, Radamel Falcao, currently on loan from Monaco.
Nani, 28, is happy to remain in his home country if United boss Louis van Gaal does not want him in his squad next season.
Ideally, United would like to sell Nani, who is under contract for another three years. But Sporting cannot afford the £15million fee.
The Old Trafford club, meanwhile, are paying a large portion of Nani's £100k-a-week wage.
