Rosenior is regarded as favourite for the Blues post after Enzo Maresca's departure on Thursday.
With Chelsea and Strasbourg both owned by BlueCo, Rosenior is viewed as a natural successor for Maresca, especially after his impressive work wit the Ligue 1 club over the past 18 months.
Speaking ahead of their clash with Nice, Rosenior was asked about the Chelsea rumours and stated: "I'm going to talk about Nice because that's my job.
"There's a lot of noise, a lot of speculation, but as a coach, if you get involved in that, you fail. My job is here, I love this club.
"No, I haven't spoken to the players about it. There's no need, they're connected and I've had a few lighthearted jokes. But we've been focused on our work. The goal is to continue creating great things here.
"In life, there are zero guarantees. You never know what tomorrow will bring. I'm just doing my job. There's already been speculation. I don't want to guarantee how long I'll be here, but I enjoy myself here every day. I intend to continue doing so as long as I'm here. I love this club, but I can't guarantee anything. Nobody can."
Rosenior also said: "I want to do my job here, it's simple. The reality today is that I am the manager of Strasbourg and I am focused on my position.
"There are exchanges because we are part of the same group. I'm honest, you can never control everything in life. I could say I'm going to stay here for years and then get fired."