The story is a typical bit of journalistic speculation, in the worst traditions of the British Press. There is not even the tiniest bit of evidence to support what it says.
The reasoning could be summed up as:
(i) tennis players who aren't doing as well as they had hoped often sack their coach:
(ii) Murray is not doing as well as he had hoped, and so is thinking of sacking his coach.
As the t-shirt says: "The Daily Mail: Reading it is like spending 20 minutes in a lunatic asylum."
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"Where Ratty leads - the rest soon follow" (Professor Henry Brubaker - The Institute of Studies)
I do of course remain cynical about anything I read in the papers and this may well be groundless speculation especially as he has always seemed very happy with his current coaching setup.
On the other hand he has now been with the current team for over 2 and half years so I wouldn't be overly surprised if he was at least considering a change.
I balance I don't think there is too much substance to the story.