The Sun are the ones reporting the story, suggesting that Clarke is in a race with Nigel Pearson and Exeter boss Paul Tisdale to succeed Kit Symons at Craven Cottage. The obvious questions here is why Clarke would jump ship to a team lower in the same division but I suppose there are a few things that might tempt him.
Money is the obvious first point, with Fulham never afraid to splash the cash to get the man they want and presumably Clarke is on fairly modest wages given the financial environment at Reading when he signed last December. Likewise Fulham might be promising him a juicy transfer budget in January and with the two teams separated by a mere four points, he might consider Fulham to be a better bet at getting him back to the Premier League sooner rather than later.
While location shouldn't really be much of an issue, Clarke has spent a lot of his life and career in London so I suppose a move back to the capital might also suit him.
Again the above is total speculation but there's certainly an argument to be made for him moving even if those reasons are slightly flimsy and speculative at best. For what it's worth the bookmakers haven't yet added him to their Fulham betting markets but on the exchanges, he's moved into second favourite at 6/4 at the time of writing.
We'll obviously keep an eye on this one but for now I'd very much file it under the unlikely column, you can read The Sun article here.