The claims come at a time in which Pogba is reportedly unsettled at Old Trafford, amid rumours he could leave United in the summer for Real Madrid.
The France international, however, was given a starting role by Mourinho for Saturday's Manchester derby, where a win for City would seal the Premier League title.
Speaking ahead of United's clash with City at the Etihad Stadium, Mourinho told Sky Sports: "Guardiola says that, the agent denies.
"So one is saying truth and one is not. I'm not interested which is the liar and which is the honest guy. I'm not interested."
When asked what his response to the offer was, Guardiola had said on Friday: "I said no. We don't have the money enough to buy Pogba because he is so expensive.
"Pogba is an exceptional player. A top, top player."
Raiola, meanwhile, denied having any contact with the City boss, telling BBC Sport : "I never spoke to Pep Guardiola. I would not speak to him about players; I would speak to Manchester City."
The player himself also showed his confusion at the claims he could have swapped one Manchester club for another during the January transfer window.
"Say what?!" Pogba wrote on Twitter on Friday , less than 24 hours before he went head-to-head with Pep's men in the title decider.