There has been speculation that Premier League outfit Crystal Palace are among those who have checked on the 23-year-old.
Ligue 1 outfits St Etienne and Nice are also said to be keen on a man capped four times by Denmark at senior level.
Brondby will not stand in Makienok's way if a tempting offer is put to them in January, but are reluctant to reveal to potential suitors how much it will take to force their hand.
"There is attention from England, but of course I do not want to say which clubs," Rud was quoted as saying by Danish tabloid BT.
"If we receive an offer, we will sit down and look at it. It needs to be an offer that we could accept.
"It will also depend on whether the offer interests Simon.
"I cannot say at the moment what we will accept. It all depends on what gets put on the table."