"It is definitely possible (that I move abroad) but you know my love for English football," the Togo international told British media.
"My experience in English football has been beautiful and I would love to ... be remembered in English football like Didier Drogba."
Drogba, a former Ivory Coast international who now plays for Montreal Impact in Major League Soccer, won four Premier League titles, four FA Cups and a Champions League trophy with Chelsea.
Adebayor, who was released by Tottenham Hotspur in September, joined Palace in January on a short-term deal until the end of the season.
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Palace face United in the FA Cup final at Wembley on Saturday and Adebayor said the game was his last chance to win the trophy.
"At Arsenal I couldn't win it with them, I went to City and couldn't win it with them, I went to Tottenham and couldn't win it," he explained.
"At my age now I have to win it. There is no way of saying 'maybe tomorrow'. There is no 'maybe tomorrow' for me.
"Now is the right moment for me. Let me go and do what I need to do to grab it."
(Reporting by Ian Rodricks in Bengaluru; Editing by Richard Balmforth)
