However, the crisis-stricken club recently underwent administration and had a transfer embargo placed on them, thus making the 34-year-old's move impossible.
Gattuso's agent, Andrea D'Amico, told Sky Sport Italia: "Rangers? It will be very difficult because they cannot sign new players older than 18 for a year."
There is no shortage of suitors for the highly-rated midfielder though, and the agent revealed that there will be more developments next week.
"He has told me to take note of all the interested clubs and we will talk more about this next week," said D'Amico, "There are many clubs all around the world who are asking for information."
Gattuso spent the last 13 years playing for AC Milan and has only played for four clubs in his career - Perugia, Rangers, Salernitana and Milan.