The Daily Mail says Moyes has been looking at players without a club and it is possible that he will add Hitzlsperger, 30, who is a free agent after leaving Wolfsburg but has played in the Barclays Premier League with Aston Villa and West Ham, to his ranks.
"I'm a bit worried we do need cover," said Moyes. "I've got to look at players who are out of contract to give us some cover over the next few months. There are not many around but I am looking without having anything specific at this time.
"The time is right to further Ross's development. It's not ideal as we need another midfielder, but I have to think longer term and he is ready for proper football. I want to see how he develops."