If signed, the agreement will keep the 25-year-old in the nation's capital until the end of the 2024 season.
"Those [contract] conversations have started and we'd like to get something sorted sooner rather than later," Woolford told The Canberra Times.
"I want to play footy in Canberra and everyone is well aware of that."
After biding his time in the NSW Cup, Woolford grasped onto a first-grade opportunity in Round 10 and hasn't let go, playing in all games since.
The Raiders rake stated his desire to continue playing at the top level and praised the welcoming nature of his teammates.
"Now that I'm here, I definitely don't ever want to let [this opportunity] go," he said.
"The boys have been really good to me. I think me and Tommy (fellow rake, Tom Starling) complement each other really well. We've got very different styles, and we're winning games at the moment, so something's obviously working."
In addition, Woolford only had positive things to say about Canberra coach, Ricky Stuart.
The emerging playmaker expressed his gratitude for the ongoing efforts his mentor has placed on his game since stepping into the senior side.
"He's encouraged me to play my natural game. It's very easy to come into the NRL and be a little bit timid but he's constantly pushing me to do more," Woolford said.
"I love playing under Stick."
With representative round now on the backburner, the Raiders' attention shifts to their Round 16 opponent, the St George Illawarra Dragons.