The experienced right-back, who has nearly 200 Championship appearances to his name, was a top performer in Wayne Rooney’s Derby team last season.
Speaking to News at Den about Byrne and the transfer rumour itself, Gary Rowett said: “We’ll have names thrown at us, there will be lots of players linked.
“Nathan Byrne is a very, very good attacking right-back in this division.
“He has been doing it for a long time in this division and his form was excellent again last year for Derby.
“What Derby will do with players that are either out of contract or have options or whatever is not my concern.
Quiz: Are these 20 Millwall transfer facts true or false?
“Again, I’ll leave all of those sorts of negotiations to Alex [Aldridge, head of football operations] and Steve [Kavanagh, chief executive].
“There are lots and lots of players on [the Lions’ list of transfer targets] so I wouldn’t really comment on whether we’re interested in specific players.”
Byrne certainly is a Championship standard player who could prove to be a real shrewd addition at The Den, however, with Danny McNamara rising at an impressive rate, there is no guarantee that he would see regular football.
With other Championship clubs reportedly in pursuit, it remains to be seen if the Lions could attract a player like Byrne with there being an element of uncertainty around minutes.
As Rowett suggests they will have a long list of potential targets that they will be monitoring over the summer, with there being a number of other positions that the Millwall manager will be eager to address.
As the summer progresses situations will change too, which could increase or decrease their level of interest.