Beye returned from a nasty ankle injury and could be back in action against Arsenal on March 21.
The 31-year-old’s current deal is due to expire in the summer of 2010.
“We will talk with the club,” he told the Evening Chronicle.
“I have one year left and I’m not the type of player who enjoys being at the end of his contract.
“We will talk to the club at the end of the season.
“I’ve given my best for the club and I am happy to be here.
“I want to play for Newcastle. I want to stay here and continue doing my best.
“For me there are plenty of things to look forward to next season and, with a settled team, without the turmoil, we can do well.
“So I hope that we can talk with the club and find a solution.”