Alexander was linked to the Sky Blues last summer.
On the rejection of his offer, Alexander's agent said
"Is Neil being greedy? Absolutely not. Neil is asking for a perfectly fair contract that reflects his status at the club.
"It is not in his mentality to be greedy or make unrealistic demands. I wouldn't want to divulge how far apart Neil and the club are in terms of agreeing the financial side of things.
"All I would say is we've entered into a process of negotiation with the club and we're hopeful of reaching a positive outcome.
"Neil has stated several times his desire to stay at Cardiff, the possibility of other clubs looking at him isn't really an issue."