Chelsea’s loss to Arsenal on Sunday means Rosenior's men sit sixth in the Premier League table with 10 games to go, three points behind Liverpool and six adrift of both Manchester United and Aston Villa.
The Blues have 10 Premier League games remaining this season as they look for a top five finish and therefore a spot in next season’s Champions League.
Speaking to talkSPORTBET Casino, Nevin has sent a warning to Rosenior as he suggests no manager is safe from being sacked by the Chelsea board.
“You can't bet against Chelsea sacking anyone. Just look at the record. But I don't think it's about Champions League football this time. For all Chelsea's willingness to change at what seems like a drop of a hat, then maybe not this time.
“People are building clubs in different ways and there are questions over whether the manager is actually that important to the club, maybe the process maybe being even more important now. Does it look to me as if the relationship between the manager and the upper echelons is in question here? No.
“Would him taking over this team at this time and maybe finishing sixth with a decently strong finish mean he should be sacked or that they will sack him? No, I don't think that either. If they had an absolute bomb from here on in then maybe.
“Is he safe? No Chelsea manager is ever, ever safe. But do I think it will happen in the summer if he doesn't get Champions League? No, I don't actually. I think he'll be fine. I think he fits well with what the ownership want.”
The goal for Chelsea is to secure Champions League football and to go as far into the competition this season as possible. However, if the side miss out on a European trophy and the FA Cup then Rosenior could be let go by an impatient Chelsea board.