I don't want to be over speculative over who said what or where the quote came from, if in fact at all, but only because of how I've seen things done over here for a very long time, do I think there's a seriousness about it.
I'm not saying he's going to get the sack, especially because while not anyone's overall target, we could still win the FA Cup and even with an incredible amount of luck finish 6th. If that was the case then I think it swings everything around, and I know 7th place is splitting hairs so I'd think they could see that as an oversight but nothing worse..
Anyways, I do personally believe 100% that Henry's ultimate goal is to attain Champions League, win that and win the league, not necessarily in that order and so if things carry on the way they are now through the end of the year with only the CC to show for it, that's just my personal belief that the "inside source" is more or less spot on, and again that does not necessarily mean the sack, but not ruling it out either..
Far as the English media and papers go, I pay almost no mind to any of it except for a few respected sources at Sky, BBC and/or when I see a club source, player, or agent give a direct quote, and even then I'm cautious unless what's being talked about makes sense on several levels. IE - Gaston Ramirez being a strong rumor to join, being Uruguayan, young, not overly expensive and having a preference for England.. vs anything that says Eden Hazard... so on, so forth.. some things aren't worth your time..