The Portuguese winger only signed a new five-year contract with the Red Devils in September but speculation emerged at the weekend linking him to Juventus.
The 27-year-old has featured 15 times for the Premier League champions this term, with his last appearance coming in the 1-0 home loss to Newcastle on 7th December.
But Conte refused to be drawn on the speculation, preferring to leave transfer dealings to the club's hierarchy.
"Nani? I'm the coach. For these things there are (director Beppe) Marotta and (sporting director Fabio) Paratici," he said.
He also refused to be drawn regarding the futures of current Juve players Paul Pogba and Andrea Pirlo, amid rumours they could be leaving next season.
In comments reported by Gazzetta dello Sport, Conte is quoted as saying: "These questions must be put to Marotta. I only think of training."
Conte is seeking to guide his side to a third consecutive title but has also challenged his players to be successful in cup competitions as well.
He added: "I'm proud of this group. In two years we have made important steps, but I'm sure that Juve won't stop here. The aim is to win also on an international level.
"Now we have three aims for this season: scudetto, Coppa Italia and Europa League."