Karipidis joined Hearts from PAOK Salonika in August 2006 and has gone on to establish himself as a key player in the side.
He is contracted to Hearts until next summer but the club are eager to tie him to a new deal and negotiations began last week.
The 25-year-old is currently back in Greece with his wife following the birth of their daughter, but talks will continue through his agent Jacques Lichtenstein.
"I had a telephone call with someone from Hearts but that is all so far," Lichtenstein told the Edinburgh Evening News.
"I think they would like to agree a new contract and Christos has not said anything different than before.
"Maybe in two or three weeks we will hear more from them.
"Christos is with his wife in Greece having their baby and I hope to speak with him in a few days."