Released by Crystal Palace last summer, Adebayor was sensationally linked with former club Tottenham last week.
It's claimed talks with Spurs have been so positive that an offer has been to the striker.
However, Lyon president Jean-Michel Aulas has also declared his interest in Adebayor this week.
"I love Adebayor," smiled Aulas. "But is it possible (his arrival)? If he really wants it, everything is possible..."