Fulham boss Meulensteen is understood to have been quoted a £3.3milion fee for 6ft 7in target man Makienok for a January transfer.
Press Association Sport understands the ex-Manchester United coach could try to prise the 23-year-old away from Brondby if Dimitar Berbatov leaves this month.
Makienok's agent Michael Stensgaard said the six-cap Denmark forward is in "no rush" to leave Brondby, and is currently fixed to a "long-term" contract.
"Obviously there is interest from a number of sources and not just from England," Stensgaard told Press Association Sport.
"We will wait to see what happens in the coming window, and then perhaps again in the summer.
"We have a very good dialogue with Brondby and we are in no rush.
"So we will make a decision to suit all parties."
Makienok has scored six goals in 12 outings for Brondby this term, taking his tally to 26 in 48 appearances since his March 2012 signing.
A number of Premier League managers are confident his towering frame would suit the English game's physicality, with Meulensteen believed to be chief among them.
Stensgaard, however, pointed out any potential transfer must allow Makienok to take a significant step forward in his career.
He said: "It's very important for Simon to make the right move.
"But there is no panic and no rush.
"If the right offer comes along then we will take a look at it.
"We would need to look carefully to ensure any club can help him reach his potential.
"We have set our specific criteria, and I'm sure Brondby have done the same for themselves, in terms of the fee they would expect."
- Sports & Recreation
- Michael Stensgaard