Nani has been out of action after breaking his collerbone just before the World Cup.
The Portugal winger could make his return against Philadelphia Union on Wednesday or Kansas City Wizards on Sunday.
Nani said: “I started full training with the team a couple of days ago and I feel very good now.
“My fitness is getting better all the time and I hope to be involved in this week’s games.
“I’m very much enjoying the tour – it’s a great opportunity for me to get a good pre-season under my belt ahead of the new campaign.”
