Hitzlsperger staying with Toffees
Hitzlsperger, having been without a club since leaving Wolfsburg last summer, signed a short-term contract with the Toffees in October that saw him through to this month.
The 30-year-old former Aston Villa and West Ham player has made seven appearances for the Merseyside outfit so far and, when asked about Hitzlsperger's future, Moyes said: "We have decided to keep him on. Thomas is going to stay until the end of the season."
Meanwhile, Moyes has reiterated that he is not looking to sell players in the current transfer window.
Everton's midfield powerhouse Marouane Fellaini has been linked with a move away from Goodison Park, with reports suggesting there is a £22million buyout clause in his contract that several major clubs could be looking to trigger.
But when questioned about that, Moyes - speaking ahead of his side's Barclays Premier League home clash with Swansea on Saturday - said: "The plan is to keep all of our players.
"I wouldn't be talking about anyone's contracts if I can help it, and I won't do it now."
Regarding potential incoming personnel, Moyes added: "We are trying - we will look around and see what we will get."