The Lions face stiff competition in the race for his signature, however, with Sparta Prague and current Czech champions Banik Ostrava lso said to be interested.
Koubsky currently plies his trade for Tescoma Zlin - who finished eighth in the Czech League last season - but is now looking for a new challenge.
Millwall's interest has been confirmed by one of Koubsky's agents, Vikto Kolar, who told Sky Sports: "Millwall are interested in him. We are talking things over but there are also big offers from Czech Republic from Sparta and Banik.
"Jiri can now move to England and so it is something he is looking at, although the lure of Champions League football is there with the others."