Being happy is not unequivocal though, is it?
I was happy at my last job but still moved on to another one because I thought I'd be even happier. Turned out I was right.
Nothing needed in writing. Just a painfully simple one line statement to then press from the Chamberlains would suffice: "I/he is staying at Saint for the rest of the season"
That said, part of me suspects that the club (Cortese) are happy to let the speculation grow (indeed, he MAY even have something to do with stoking up the story) as we'll come put the other side as a force to be reckoned with (if he stays of course)