"Some situations fit together nicely, and they did here, but I can't say whether they are going to or not with Rangers," said Dyche. "Of course he wants it to work there.
"That's for other people to decide and his relationship with the management team there, that's all for them and not for me. I can only speak of his time here.
"I was thankful for what he did and I think he enjoyed what he did here and he enjoyed the group he was working with. He's gone on to pastures new."
"He made that choice [to leave] - there's no angle between me and him and the club and him," Dyche added. "He felt it was a new challenge and it has turned out to be a new challenge, whatever way you look at it.
"It's a massive club who are working hard to get back to where they belong which is certainly around the top of Scottish football, that's for sure."
Asked whether he would take Barton back, Dyche said: "He's nothing to do with me, he's part of Rangers football club."