The 26-year-old West Australian, who is the No. 7 defender in the Official AFL Player Ratings, is out of contract at the end of the season.
However, he is not a free agent, so a move to West Coast or Fremantle would have to come via a trade.
Asked on Melbourne radio station Racing & Sport on Tuesday morning if he is going to stay at Geelong, Taylor replied: "I really hope so.
"We've just got some personal things to sort out, my wife and I and our family.
"If we can get all those things sorted out, then hopefully we're going to be at Geelong a fair bit longer.
"But I think you can appreciate that when you've got young kids and a wife and you're all from 3000 kilometres away, you don't want to rush these decisions.
"You want to make sure that you get them right, and you've got to think of your family as much as yourself in these situations."
Taylor has become one of Geelong's most important players since being selected by the Cats as a mature-age prospect in the 2007 NAB AFL Draft.
Having made his name as a defender, the 2010 All Australian is now frequently used as a swing-man up forward, and he has made a big impact in attack the past two seasons.
A member of Geelong's 2009 and 2011 premiership teams, Taylor has played in 96 wins in his 120-game career.
"We've got a great team, we've got a great leadership group, we've got a great coaching group, and it's an amazing place to be around," he said.
"When you win so many games of football in a short period of time, which I've been lucky enough to be a part of, it seems pretty silly to run away and take off.
"But as I mentioned, there are some personal things that we need to make sure that we get right first, and the health and wellbeing of your family is pretty important.
"Looking after your family is a really important thing, because they're going to be there hopefully for a long time.
"And I just want to make sure they're happy wherever I choose to play my football."
Although the contract negotiations continue to drag on, Geelong is very confident that he will remain at Simonds Stadium beyond this season.
"I'm really comfortable with the way these things work these days, certainly at our club," Cats coach Chris Scott said on Tuesday.
"Harry and I and the other powers that be at our club have really frequent and open discussions.
"I'm loathe to say that I'm too confident, because that might sound like I'm putting pressure on Harry, but I am.
"Harry and the club are in a really good place. We understand that other clubs would love to have him on their list, and they can go their hardest."
Adam McNicol covers Geelong news for AFL.com.au. Follow him on Twitter at @AFL_AdamMcNicol
