The 30-year-old, who scored nine goals last season, has been offered a new 12-month deal by the Cumbrians, but was given until midnight on Friday 31 May to make his decision.
However the Scot, thought to be on holiday, has failed to let boss Greg Abbott know, and the club are keen to get the issue sorted as soon as possible.
"Lee Miller technically had until midnight on Friday to let us know what his intentions are," Abbott told the club's official website.
"We think he was away as that deadline came, and it's something we will pick up again early next week so that we can find out where we all stand.
"It's understandable that he had to take some time away, given the situation, but he also knows that we need to know what his thoughts are. We would expect the situation to be resolved when he returns from his break."
- Sports & Recreation