The Newcastle centre-back's current contract expires at the end of next season and he rejected the club's initial offer back in September.
But chairman Chris Mort has confirmed the contract deal will be sorted soon.
Taylor: "I'm a Newcastle United player for 13 more months and hopefully I'll get a new contract, that's what I'm playing for now.
"We've got one more game left this season, and then we'll take it from there.
"Hopefully we can come to some agreement, I'm sure we can. Everyone knows I want to be at the football club, so we'll take it from there.
"He's (Keegan) got the respect of every single player, the staff and all the people involved with the football club. The fans absolutely love him.
"This club will be moving forward, and hopefully next season with Kevin Keegan it will be.
"It shows how much he loves this club, he wants this club to succeed. We are going forward and the form of late has been good.
"At the start of the season our performances weren't the best, but the fans stuck behind us through hard times.
"Of late, they've been absolutely fantastic, and hopefully next season we can give them something to shout about."