The 25-year-old Dubliner looks set to leave following nine years at Turf Moor, during which time he progressed through the youth ranks and went on to make 269 appearances.
McCann's current deal expires this summer and Dyche revealed the reported Norwich, Celtic and Blackpool transfer target has shunned the opportunity to discuss staying for a testimonial season.
"Chris McCann's situation is that he actually didn't really want to engage in a contract situation with us, so that was clear on that one - not because he dislikes us or the club but because he feels that it might be time for him to move on," the Burnley boss told the Lancashire Telegraph.
"That situation might change but that's how he's felt about it so that's a natural situation and progression of contract situations, but that can change rapidly.
Indeed, Dyche holds no malice against McCann for this state of affairs and refused to close the door on the possibility of him remaining with the Clarets.
He added: "At first you've got to want people who want to be here. He hasn't said that he definitely doesn't want to be here, but he didn't want to enter into contract negotiations, basically to see what's out there.
"That shouldn't be held against him by the way, that's just the reality of modern players, of modern contract situations, agents and all the rest of it. It's just the business side of football."