Kayal has fallen out of favour since Ronny Deila took over, making just 13 appearances for the Scottish champions, and Brighton have acted quickly to take advantage of this during the January transfer window.
The Israeli international midfielder has reportedly agreed terms with the Seagulls and he is due to undergo a medical at the Amex Stadium tomorrow.
Brighton have improved under the guidance of Chris Hughton, but they are still on the lookout for additions in the coming weeks and Kayal could be a good buy.
A combative and energetic presence, he has Champions League experience and should bring a lot of quality to the South Coast club's side.
Kayal only has six months remaining on his contract at Parkhead, meaning that the fee agreed is unlikely to have been too large a price.
If signed tomorrow, as expected, Kayal could go straight into the Brighton team who face Arsenal in the FA Cup on Sunday.