Both Liverpool and United made enquiries about the possibility of signing the Israel international three years ago after he arrived at Celtic from Maccabi Haifa in 2010.
However, the 25-year-old has since suffered a string of injuries and has been limited to just four SPL starts so far this season.
But the central midfielder has revealed that he is still keen on sealing a switch to Anfield or Old Trafford.
“In my first season at Celtic a lot of teams came to watch me,” said Kayal.
“Kenny Dalglish, who was manager of Livepool, and Sir Alex Ferguson at Manchester United had communications with me.
“With a lot of teams interested, Celtic wanted too much money. Now, because of my injuries, the price is much lower but my dream is still alive and well.”
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