Why not say he's off on a free as they weren't prepared to pay his demands, and they think they can improve their squad with someone else better for the money. That's just business. Why make such strange announcements about their honourable business principles? They furloughed people for damn's sake - they're just about the making of money.
Articles like this are very indicative for them though. They are about as sly, deceptive, untrustworthy and outwardly spivvy bunch of people as you will ever meet. So they are not going to frame things as "we've got no money". There is a spin going into it, that it's somehow within their hands.
When you boil down the multitude of context and spin though, what you have is a club who can't afford to keep one of their best players, who has played pretty much every game this season, and then trying to spin that story.
If they can't afford to keep Wijnaldum as he's nearly 30, it's going to be very interesting to see how these contract negotiations go for Salah, Mane, Firmino, Van Dijk, Fabinho all go.
Due to age pressures (all either approaching or older than 30 come the summer) and the pandemic all will have lost anywhere from 50-75% of peak value. Whatever value is left, will then start to massively decline the day they go into tghose final 2 years. Thats the real countdown point.