Liverpool have spent big this summer, bringing in Fabinho, Naby Keita, Xherdan Shaqiri and Alisson, leading to Mourinho to make his controversial remarks.
"Liverpool are trying to win the title with their amazing investment," Mourinho said earlier in the week.
Thompson has responded in kind, speaking on 'Sky Sports' Soccer Saturday program: "Pot and kettle? Oh my goodness.
"You always buy what you can afford and it's net spend at the end of the day. Our net spend compared to United's net spend is massively different.
"How can he say that? Is he just trying to wind people up because this is Jose? Liverpool trying to buy the title? Oh my goodness, I can accept that from some other clubs and managers, but not from Jose Mourinho.
"Just because we've spent some money this summer? It was absolutely outrageous comments coming from Mourinho, whose bought titles everywhere he's gone."