There's been reports that Dyche fell out with the Burnley board and is set to leave in the summer.
Yes he was very angry that 1) the contracts of several first team players were left to run down and expire after a failure to agree extensions, and that 2) he apparently will not be given a lot of money to spend when the transfer window opens at the end of the month even if Dwight McNeil is sold.
He has done a wonderful job there that's for sure. In-between his appointment in late 2012 and his first promotion to the Premier League in 2014, the club only paid a transfer fee for one player in 3 transfer windows (Ashley Barnes).
Then ahead of their 2014/2015 Premier League campaign, he was perfectly happy for money to be diverted away from this transfer budget on to improving the training facilities and the infrastructure behind the scenes. Most other managers in that position wouldn't have been so happy. So that 2015 relegation wasn't really a failure at all.
They returned to the Premier League in a much stronger state in 2016, and since then I've never thought that they could be relegated under him, as they always seem to pull out important wins when it really matters, and when they find themselves under some pressure. Plus they usually enjoy at least one big-ticket win over a heavyweight team each season.
The 7th place finish 2 years ago was an outstanding achievement given that they had amongst the smallest financial resources including one of the lowest wage bills in the whole league, and looking in good shape to at least finish in the top 10 again this season (ahead of Everton's whose financial resources and spending have completely dwarfed theirs) is also excellent.