Miller, a free agent who has been testing his market value with other teams, reportedly has been offered a two-year Cardinals contract worth about $6 million overall.
Bob Ferguson, Cardinals vice president of player personnel, said he will do what he can to get Miller to re-sign -- the team's avowed wish for weeks now -- but hinted that time may be running out.
"Jamir has to understand what his market value is, and we appreciate that," Ferguson told The Arizona Republic on Monday. "But we have an offer on the table and we've got to do something in the next few days, or we have to move on."
Miller, the Cardinals' leading tackler last season, visited the New England Patriots and the Chicago Bears. Tennessee talked with his agent, Steve Baker, but didn't schedule a visit.
Patriots coach Pete Carroll told the Republic he likes Miller but won't pursue him further for now.
"It really is going to depend on what happens with Arizona," Carroll said. "We wanted to find out where he was because he's a quality player and can help a club.
"But we're not going after it (a contract) at this time," he added. "We're just going to monitor what takes place in the Arizona negotiations. To attract him right now is more than we want to pay."
Carroll said Miller made it clear he wants a situation in which he can serve more extensively as a pass rusher than he can behind Andre Wadsworth and Simeon Rice with Arizona.
"You could use Jamir as an outside rusher in nickel situations. That's what he wants," Carroll said. "He's also played nickel linebacker behind the line of scrimmage. He's done a lot of things. That is what makes him attractive. He's a very flexible player.
"His heart is set on rushing the passer right now," Carroll added. "That's why he's hesitant to fully commit to Arizona, because they can't promise him that."
That's right, Ferguson said.
He said he believes in what Miller can do "but nobody's going to design a defense for him."
"He's a young player who can come back in here with an up-and-coming defense and really establish himself, but we will determine what we are going to do if and when he signs," Ferguson said. "There will be no promises."
Even so, he added, "we've made it clear that we want Jamir back."
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