Asked how off-field staff at each club will be feeling right now, Wyness said: “It’s just a very worrying time.
“There will be people, especially in the present financial climate, who will be very concerned, and that will translate into their job performance.
“It’s so important for the leaders off the pitch in the club to be able to handle this with great humanity.”
BBC London asked both clubs what plans are being drawn up to prepare for the possibility of relegation but they declined to comment.
Wyness said: “I hope they are planning properly, and not just paying lip service to it.
“You’ve got to be getting all your consultations ready in terms of layoffs and all that sort of thing, and I’m afraid it’s just not pretty but this is the time to focus and be professional.”
With so much at stake beyond the confines of the pitch, the stars of Tottenham and West Ham will be playing for far more than professional pride over the next few weeks as they bid to keep their clubs in the Premier League.