The Eagles made a deadline day approach back in September, according to Brondby, but were unable to put a loan agreement in place.
It is reported that Makienok remains in their thoughts heading into the January window, despite Ian Holloway having been replaced at the Selhurst Park helm by Tony Pulis.
They are unlikely to be the only ones looking at the 23-year-old striker, though, and Brondby will consider all offers put to them before taking a decision on the Denmark international's future.
Sporting director Per Rud told Danish tabloid BT: "If any serious offers come in for Simon, we will consider them.
"We have promised Simon and ourselves that. We owe our investors to consider them in case we can reach an agreement regarding a transfer.
"But we are really happy to have him in our team and would like to keep him. We don't need to sell."
He added: "It is correct that Crystal Palace called five minutes before the transfer window closed to propose a loan deal.
"Since then, we have not heard from them. But it would surprise me if they and other clubs are not keeping tabs on him."
Rud also claims that Brondby have started to look at possible replacements for Makienok, with it looking increasingly likely that he will be on his way out of the club in the New Year.
He said: "Of course, it is my duty as sporting director to always keep track of what is going on in our squad.
"I have already discussed all possibilities with our coaching staff."