The Reds manager is continuing to look at ways of adding to this squad following the arrival of Wilfried Zaha and Guillermo Varela this summer.
Reports that Bayern Munich are close to signing Thiago Alcantara from Barcelona were said to be a blow to Moyes' transfer plans, even though he has a policy of not commenting on players from other clubs.
"We're on with targets that we are chasing at this moment in time," revealed Moyes at a press conference in Bangkok. "There are people we are actively chasing and, at this moment in time, we're happy with how things are going."
When asked directly if Thiago was still a target, he replied: "I never said at any time that he was."
Moyes also brushed off the latest questions about the future of Wayne Rooney, after Chelsea manager Jose Mourinho expressed an admiration for the England international on Friday.
"People are entitled to talk about good players," he insisted. "I'm sure Jose has been asked about lots of players as well. I'll keep repeating myself: Wayne is a Manchester United player and he'll remain that."
The likely absence for Rooney due to his hamstring injury is expected to be "two or three weeks" and he will work in the gym and pool in Manchester.