The newly promoted Premier League club snagged summer signing Sammie Szmodics from Blackburn Rovers.
And McKenna admitted that Szmodics was a player who had been on his radar for a couple of years.
“I think it’s probably been there over the last few seasons,” he told reporters.
“I’ve only been here for the last couple of seasons and Sammie’s been a very good player in the EFL for more seasons than I’ve been involved in it.
“Maybe in my first full summer here, I think he moved to Blackburn when we were in League One, so he wasn’t on our radar that season. I think Peterborough got relegated that season and I think he’d earned the right to go back to the Championship.
“And then over the last two seasons competing in the Championship, he showed what a good player he is, what a goal threat he can be and I think when he is a local player who’s got a history and an affinity around the area and around the football club, I think it’s always a nice bonus when you can have someone like that around the place.
“But that’s a small part of it, I think the bigger part of it is he’s a player who has worked ever so hard on his career to get to where he’s got to, to have the seasons that he’s had over the last couple of seasons and rightfully earned the shot to play in the Premier League.
“And for us as a newly promoted team, bringing in someone who can be the threat in term of goalscoring that he is but also work very, very hard for the team, I think that’s the type of profile that was always going to be attractive for us, and that’s why Sammie’s here.”