Murphy, 31, sees his current contract run out in the summer along with Franck Moussa, Cyrus Christie & Mark Marshall.
Speaking to The Coventry Telegraph, Murphy said: “I had a word with the gaffer last November just to see whether I had a future here because last year a lot of the lads found out after the last game of the season.
“I’m 32 now, not 18, and I needed to know if there is anything here for me, so we sat down and had a chat and he said yes and that we’d sit down before the end of the season and speak again.
“Things could have changed, I don’t know, regarding how he feels about me but for me it’s about playing football.
“I just want to keep playing football for as long as I can. I enjoy working with Steven Pressley, I enjoy the way he plays the game and I like the lads here.
“I probably feel like the old man of the dressing room but I enjoy it here and I am sure we will sit down and talk about it soon because there’s not long left; just five or six weeks, so we’ll see what happens.”
“I’m happy here at Coventry,” he said. “I’ve had my chances five or ten years ago so it’s about wanting to play for as long as I can now. I have played nearly 500 games in my career and I want to keep going.
“I’ve only missed one league game in the three years since I’ve been here so, touch wood, if I can keep myself fit I still feel I have got a few years ahead of me.”
Since joining the Sky Blues in June 2011 from Scunthorpe United whilst City were still in The Championship, Murphy has only missed one league game and has been one of City’s key players this season with a number of vital saves, including stopping five of the twelve penalties he has faced.