The 30-year-old, who has 52 caps for Germany, has spent the past week training with the Toffees in a bid to earn a permanent contract.
Moyes told the club's official website: "It is going to be a while until we are able to make a decision. He is building his fitness.
"He is enjoying doing the football work and we will step his work up next week but there will be no quick decision on that."
Hitzlsperger has an abundance of Premier League experience, having previously played in England for both Aston Villa and West Ham United.