Club captain Heaton, 32, lost his first choice spot to Nick Pope at Burnley early last season after suffering a shoulder injury and then a pre-season knock this year sidelined him and allowed Hart to take over the between the posts.
With Pope, who was in England's World Cup squad in Russia, expected to return in the coming weeks from his own shoulder injury, Dyche will find himself with three England international goalkeepers to choose from.
Heaton said he would be prepared to move clubs to get back into regular action and Dyche was understanding of that view, although he cautioned that he may not leaving mid-season may not be straightforward.
"In due course whatever needs to be worked out we will find a way of working it out," the Burnley boss said at a news conference on Thursday.
"He knows for as long as he can know that he has a future here, it's just what part of that future is right for him at this stage.
"I think he's being realistic. Me and Tom go back a long way, he was my first signing here, so we've got an open dialogue about what's going on," added Dyche who said Heaton had been "very unfortunate".
Dyche said he had talked to Heaton but suggested a January solution might not be easy to find.
"I think there's been some factual conversations, he's a good guy to speak to. It's different with Tom, I've known him virtually since I've been here and he's known me equally so they’re not difficult conversations.
"The outcome might be difficult to find because I think he's top class and I want him here," he added.
Heaton joined Burnley from Bristol City in 2013 and has made 169 appearances for the club and been part of two promotion winning teams.
But the former Manchester United youth team product, a popular figure with Burnley fans, accepts that the arrival of the experienced Hart and impending return of the highly-rated 26-year-old Pope, means he faces a tricky future at Turf Moor.
"It doesn't need a rocket scientist to see that it's going to be difficult to fit us all in," he told the Sunday Mirror.
"Come the January transfer window, I’ve got to keep my options open. The one thing I’ve been consistent about in my career is moving clubs in order to play games," he said.
(Reporting by Simon Evans; Editing by Keith Weir)
