The 21-year-old is likely to leave Mourneview Park in next month's transfer window, with a clutch of clubs said to be chasing his signature.
Port Vale had a bid knocked back last week by the Glens board, although they have come in with a renewed offer, while Blackburn are another team linked with the Northern Ireland Under-21 internationalist.
Hamilton said: "Hibernian, Port Vale, Blackburn - I could reel them off. There have been loads of clubs watching.
"As of yet, we’ve only had one bid which was knocked back ten days ago."
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Sykes is a box-to-box midfielder and is widely regarded as one of the best prospects in the Northern Irish league. Glenavon assistant manager Paul Millar said of the player recently: "Mark Sykes is the best young player in Ireland and, on top of that, he's a real smashing fella. I love him. He can head, he's two feet, can dribble, pass, score goals and he gets lumps kicked out of him every week."
Sykes' former Glenavon team-mate Bobby Burns secured a move to Hearts last summer and is currently on loan at Livingston.
Hibs head coach Neil Lennon is keen to bolster his squad in January, with midfield one of the priority areas of his team.