The former Brighton forward took a dig at the Merseyside club on social media this week.
Maupay joked on X: "Whenever I’m having a bad day I just check the Everton score and smile.”
“I think it is fair to say there is a bigger picture to Everton Football Club that I am focusing on and I don’t think I need to be too worried about his comments," Dyche said in response.
"I don’t think we’ll be worried about that," he added when asked about taking any action against Maupay.
“There are (financial) parameters, the owners have made that clear," Dyche added on his transfer plans.
“The one thing it’s unlikely to be is hundreds of millions of pounds, whether you have got it or not – and our owners are pretty wealthy.
“Forgetting about the numbers, I’ve been doing this a long time in the Premier League and notoriously January is very tough. I’m not saying no, but it’s tough and you’ve seen it down the years. Usually, if big deals are done they pay a lot of money for those deals to happen.”