The 30-year-old has been linked with the newly crowned Ghana Premier League champions, although the Hearts have not made an official bid yet.
Awako will become a free agent at the end of the football season and is ready for a new adventure with Olympics' city rivals.
"My doors are opened for Hearts of Oak, even Harry Kane is leaving Tottenham Hotspur with the ambition of playing in the Champions League. Every player wants to explore on a higher stage," said the midfielder on Angel TV.
The former TP Mezembe player has enjoyed a good campaign with the Wonder Boys, helping them finish sixth in the just ended Ghana Premier League.
However, Hearts are interested in the services of the Black Stars player as they bolster their squad for next season's CAF Champions League.
The Phobians are also reportedly interested in Kwame Peprah of King Faisal and Asante Kotoko's Felix Annan. Read Full Story