The Barnsley manager has made signing a new centre-half a priority during the current transfer window.
Flitcroft told the Barnsley Chronicle: "We outlined what the future could look like if he signed and he was positive.
"I want Adam to think intently about the decision because it is a big one. He is one of four or five defenders that we have sat down with.
"We are looking for a centre-back and maybe someone who can play at right-back as well. We're just waiting for agents to become more sensible and realistic. We'll spend money but not waste it."
The 28-year-old has spent his entire career at the Seagulls, having joined the club's youth set-up as a 10-year-old in 1994.