Figo is currently an ambassador for another of his former clubs, Inter Milan.
He said: "They are just rumours and such statements are baseless because, until now, nobody has offered me a return to the club.
"[Madrid special advisor Zinedine] Zidane has not invited me back, so I cannot accept anything.
"It's news coming out that has no foundation. At this moment I am happy at Inter Milan."
Figo would be open to a the possibility of linking up with his Madrid coach Jose Mourinho - his former coach at Inter - in the future, though.
"In the future you never know what can happen," he added.
"On a personal level I had a fantastic year with Jose, which I enjoyed and we won major titles. It is therefore logical that, if in the future it were to happen, I would be very happy."