Balmer, who is yet to play for the Northern Ireland senior side, is said to be discussing personal terms with the Selhurst Park side as the bid to conclude the deal.
The 21-year-old has made a real impact at Inver Park since joining from Ballymena United in June last year.
So much so that he penned a contract extension last season extending his deal until the end of the 2023/24 season.
It seems though that Balmer will not see out that deal with a move to Patrick Vieira's side now in the offing.
Larne will be sad to see a player of Balmer's quality depart but boss Tiernan Lynch will be thrilled to have played a big role in his development
“Kofi has proven the quality we knew he had since his arrival in the summer,” Lynch said following the completion of his contract extension last season.
“We felt full-time football would really help him to continue his progress and Kofi feels that himself.
“For someone of just 21 years of age he has a lot of experience in the senior game under his belt. Like any young player he knows he has plenty of developing to do and he is working hard at that every day."