The England international, whose existing deal expires in the summer of 2009, wants the situation resolved as soon as possible.
Speaking at the Champions League draw in Nyon, Switzerland, Kenyon said: "The discussions that we'll have with Frank will be kept private and that's important.
"Both parties have made it absolutely clear we want to find a resolution.
"Hopefully we'll do that sooner rather than later."
Asked if the parties could arrive at a resolution before the end of the season, Kenyon added on Sky Sports News: "Anything's realistic. I just don't want to add more speculation counting down each day to the summer."
"We're committed - as is Frank - to finding the right solution to keep him at Stamford Bridge."