Following 17 days without a game, the Blues will return to Premier League action at the Vitality Stadium on Wednesday night (7.45pm ko) before hosting Wolves at Portman Road on Saturday.
Asked for an update on Conor Chaplin, who hasn't played in 2025 due to a troublesome knee issue, the Blues boss said: "Conor's trained with the group over the last week so that's a positive. So he's not going to be too far away from this week.
"We've got a few in and around it that are going to be pretty close decisions for this week to be honest."
Right-back Axel Tuanzebe suffered a fresh hamstring injury set-back at Nottingham Forest at the start of March and subsequently underwent further surgery on his thumb.
"Axel's done a little bit of training now with the group which is a positive but we have to make judgements on this week."
The Blues boss continued: "Kalvin Phillips came off with a gash in his foot (last time out against Nottingham Forest). It was 20 plus stitches, a pretty serious gash, so he hasn't been training with us. But he isn't too far away now, so again that's a judgement to make.
"There's a few others in that boat as well. We're assessing people over the next 24 hours to see who's going to be available for the first game (Bournemouth) and if anyone doesn't make the first game then there'll be a possibility they'll be available for the second (Wolves)."
Asked if all his players had come back from international duty unscathed, McKenna said: "We have one or two that are still being assessed to be honest. So we have one or two doubts going into Wednesday night."
On goalkeeper Aro Muric, who has been away with Kosovo, McKenna said: "Aro's seeing a specialist. He's looking at shoulder surgery. It's a different shoulder than what he has been having some treatment on over the couple of weeks beforehand, so it's completely unrelated and very unfortunate. If he has the surgery this week then that'll certainly be a good period of months."