The 29-year-old’s current contract with the U’s is set to expire at the end of the season.
“It’s my third season at Colchester and I’ve always enjoyed myself here,” he told the Daily Gazette.
“I’ve spoken to the manager and expressed my desire to speak with him about my contract.”
Colchester manager John Ward is keen to keep the goalkeeper at the club.
Williams is now waiting to meet Ward and club chairman Robbie Cowling for talks.
He said: “He’s agreed and said that he’ll come back to me, so that’s where it stands at the moment.
“The plan is to stay at Colchester and I now need to speak to the manager and the chairman.”
