Ronaldo, 37, has been available on a free transfer since the summer, with United hoping another club will take on his £500,000-per-week wages, sources have told ESPN, but the club have only received interest from Saudi Arabian team Al Hilal.
"Ronaldo is a top player, he is a Manchester United player," Amorim said on Tuesday ahead of Sporting's Champions League clash at Tottenham.
"Everybody at Sporting dreams of the return of Cristiano. He is a Manchester United player. I think he will be for a few [more] months. We don't have the money to pay his wages."
Ronaldo was dropped for last weekend's draw with Chelsea after refusing to come on as a substitute against Spurs and was told to train alone with United fitness coaches. However, the forward was allowed to rejoin the squad on Tuesday and could be in line to return in United's Europa League game against FC Sheriff.
The Portugal international requested to leave United in the summer to play Champions League football, provoking links to his first professional club, Sporting, although Amorim has said a move is unlikely.
Ronaldo, who has made just two league starts this season, is under contract at Old Trafford until next summer, with an option to extend for a further year.
"He is happy in Manchester, but he is not playing so that's the problem," Amorim added.
Ronaldo was United's top scorer last season with 24 goals, 18 of which came in the Premier League.
In contrast to his club status, Ronaldo remains a crucial part of the Portugal squad and will captain the country at the 2022 World Cup, which kicks off in Qatar in on Nov. 20.