Brown’s contract expires at the end of the season and the England international has rejected all offers of an extension so far.
“We would clearly want Wes to stay,” said Gill in the Daily Star.
“He’s a local boy who has come through the ranks. I think he wants to stay.
“We’ve made him what we believe is an excellent offer, but we’ve not reached an agreement. So we’ll see how it unfolds.”
He added: “It is unlikely that a club would come in and offer something substantial for him when he is out of contract in the summer.”