Iroegbunam joined from rival Aston Villa this summer and has so far impressed against Coventry City and Preston North End during preseason.
The 21-year-old has caught the eye of Dyche who will be analysing his squad ahead of his next campaign.
Speaking to evertontv, Dyche opened up about Iroegbunam and how he can influence the side this year.
“(I’m) very pleased. I mentioned to him when he came in that Premier League fitness is a jump up from when he was on loan in the Championship. We’ve spoken to him about that, so it’ll have done him ever so good to get two 90s in a week.”
“I thought he was very good again today and he’s settling in nicely. He wants to get turned, wants to play forward and wants to get a foot in when he can. He’s doing the things that I think are appropriate for how we want to play.”
He also spoke on Iliman Ndiaye and how he has adapted to the club.
“(Iliman) was looking sharp when he came on. Again, he’s learning about the Club and learning about what we do.
“There were some really good signs (in the game). Much better signs. I was expecting it, but I’m pleased it’s there because it did look a whole different outfit.”
The Toffees manager went on to say that the team needs to work harder in preseason and the preparation for the Roma game coming up.
“Building up through the week, there will still be pockets of hard work, but more sharp work now.” he added.
“Not so much the heavy stuff – it will be sharper, mentality based, technically and tactically based, going into the Roma game. Then, obviously, there’s prep for the beginning of the season.”