Hill-Wood has confirmed that Arsenal will not be meeting the demands of Gallas - who is out-of-contract at the end of this month.
The French international wants at least a two-year deal, which goes against Arsenal policy as they generally do not offer more than 12-month contracts to players over 30.
At 32, Gallas has only been offered a one-year extension - which he has thus far refused to sign.
"He is asking for too much for too long," he said.
"Players are going to have to learn some time that money doesn't grow on trees."