The Wales international has not yet played due to an injury he sustained during preseason.
But Broadhead is fit enough to likely get a place on the bench against the Saints at the weekend.
“Pretty much everyone’s been involved with training in some part this week,” McKenna said to reporters.
“We’ve got a few players managing different knocks and different issues but everyone’s played some part this week.
“Some are a little bit further behind who have missed pre-season, but the group’s looking really healthy.”
On Broadhead and Harry Clarke, he added: “Both have trained this week. Nathan’s a little bit further along than Harry. I think from a physical point of view, he would be able to play some minutes this weekend, which is a big positive to have those options.
“Harry’s still a little bit further behind but he’s trained in the majority of the sessions this week, so if we were in big, big need he probably could be able to get on the pitch for some minutes this weekend.
“But we’re pretty strong in that position, so it gives us good depth now and we know we’re in a period where there’s not that many games at the moment, so it’s a period for us to train and develop the squad and go at one league game a week 100 percent.
“But there’s going to come times over the course of the season where the schedule gets busier or we’re shorter on numbers now and we’re going to need everyone to make contributions and it’s great to have those options.”