The 24-year-old recently picked up the club’s player of the month award for August and has impressed since the start of the season.
Kilman has kept his place on the right side of the back three, despite being left-footed, but has put in composed performances while Willy Boly and Yerson Mosquera have been out injured.
Since Boly has returned he has been unable to force his way into the side and Kilman is solely focused on keeping his place.
“Of course (I’m pleased with my run in the team) but I need to keep my head down and not get carried away with it.
“I need to keep working hard and always keep improving.
“It’s been fantastic (working with Bruno Lage).
“I’ve been working hard and staying focused. I’m trying to keep working hard, improving and getting better and hoping to stay in the team to do my best for everyone.”
In response to his impressive performances, some Wolves supporters have been putting Kilman’s name forward for a potential England call-up – but the defender is refusing to focus on that for the time being.
When asked if he was thinking about an international call-up, Kilman added: “No, not really to be honest.
“I just want to perform well week in, week out for Wolves.
“If things like that come in the future, then they come in the future. I’m not worried about it now.
“I’m just making sure I keep my head down and do my best for Wolves.”
Kilman put in a solid performance again as Wolves beat Newcastle 2-1 on Saturday, as Raul Jimenez and Hwang Hee-chan combined twice, resulting in a brace for the latter.
“Every game in the Premier League is tough and we really had to manage the game towards the end,” Kilman added.
“I thought in the first half we really dominated possession and we had some good chances.
“If we, maybe, scored the second goal of the game then the game would have been a bit more comfortable. Newcastle have some great players, had some good chances and they scored, so we had to show our resilience to come again and get another goal.
“It was some superb play from Raul and Chan, it shows the quality we have in the squad. They are fantastic.
“Raul’s hold-up play and Chan moving off him, it is working really well at the moment. It’s been good to watch.”
Kilman spent several minutes down injured in the second half as Boly warmed up to replace him, but eventually he was able to continue.
When asked if he was OK, Kilman said: “Yeah all good.
“It was nothing serious, everything is fine. I’m glad I managed to finish the game.”