Slot was dismissed at the end of May, only a year after leading the Reds to their 20th league title, following a disappointing fifth-placed finish in his second season in charge.
Speaking on the talk show Vandaag Inside, Van der Gijp said reports had reached him that Slot was effectively "spat out" by his own players within the space of a year.
"It's strange, isn't it? That you hear stories that Slot was really thrown out at Liverpool. In one year's time. How do you manage that?" Van der Gijp said.
Presenter Wilfred Genee pushed back, saying he had heard no such stories, while fellow guest Maurice Steijn also appeared surprised by the claim.
"Basically it comes down to the whole squad feeling things were going badly, but it was never Slot's fault," Van der Gijp continued.
"They all got a bit sick of it, really. I think: you have to pull that off too."
Genee remained unconvinced and pressed Van der Gijp on his sources.
"Are you sure about that? Who did you hear that from?" Genee asked.
"I'm sure. But that doesn't matter," Van der Gijp replied, adding that only Virgil van Dijk, the Liverpool defender, appeared to have stood by Slot throughout.
Genee continued to probe, asking whether the claims had appeared in the English media.
"You just hear it, don't you? From lads who worked with him and sat in the dressing room," Van der Gijp said.
Fellow panellist Johan Derksen backed his colleague's version of events.
"If René has a good source, I believe it. Slot is of course a proper schoolmaster type. With those kinds of players you shouldn't talk at them too much," Derksen said, adding that Liverpool forward Mohamed Salah's body language had also told a story of its own.
Sky Sports pundit Jamie Redknapp offered a similar reading of the dressing-room dynamics at the time of the sacking, suggesting player power had a role in Arne Slot's sacking by Liverpool, even as he backed Andoni Iraola, the frontrunner to replace him, to handle the pressure of the job.