A report in a national paper yesterday said the experienced defender has yet to agree terms with the club - and suggested he was a target for other sides in the first division.
But although contract negotiations have yet to begin, a chat with Ton boss Allan Moore means the 31-year-old knows he is wanted at Cappielow.
McCaffrey, pictured, told the Tele: "I've had a very informal chat with the manager, just in passing really, but there's been nothing more to it than that.
"I haven't actually spoken in any detail with the gaffer or the chairman. But I'm happy at Morton and the gaffer seems to be happy with me, so that's the main thing.
"I'm enjoying my time so far and am looking forward to the rest of the season, so I'm hopeful if I continue to do well then these talks will take place.I'm enjoying my time here and I hope it continues, that's all I can say. I'm hopeful I'll be here next season too.
"One of my pals phoned me to say there was a wee bit on me in the papers. I think someone has maybe got in touch with my agent and he said I hadn't signed anything."
This sense of contentment means there is no urgency to get around the table, but the Ton captain is still eager to have his future sorted out sooner rather than later.
He added: "I don't think there is any mad panic. The only thing I would say is that I'm in a situation where I'm married and have bills to pay like everybody else.
"So the sooner I get my future sorted out the better. There really isn't a great deal of time left in the season, maybe only about four-and-a-half months."
And while McCaffrey is comfortable with life at Cappielow, he understands rumours will be commonplace as other managers begin compiling lists of future transfer targets.
He said: "I think teams are obviously looking to strengthen at the moment to make a push towards the end of the season.
"Managers are starting to have half an eye on next season as well and are planning for the near future."
Meanwhile, goals from Brian Graham and Stewart Kean gave Ton a 2-1 win over East Stirlingshire in a bounce match at the Ravenscraig sports complex yesterday, with Moore also fielding a number of youngsters.