The Greek international made a favourable impression at Ibrox during the final few months of last season, but the Glasgow club are struggling to push through a permanent deal for the Panathinaikos full back.
Wanderers manager Sam Allardyce told the Daily Record that he does hold an interest in Kyrgiakos.
"We have had an eye on the player for quite a while but we've not taken it any further than that.
"We've been watching what he's been doing with Rangers with great interest but I know nothing about the situation between them and Panathinaikos.
"Obviously, though, it would be fair to say that Kyrgiakos has interested me for some time - I can't deny that."