The Sun says even if Chelsea miss Champions League qualification, Rosenior could yet be retained for the new campaign.
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It emerged this week that the board had lost confidence in Rosenior and were questioning if he had the qualities to manage the team long-term.
But it's now suggested no hasty decision will be entertained and that Rosenior will be given every chance to prove himself.
The Blues ownership are wary their reputation is tied up in Rosenior after the way they sacked Enzo Maresca and replaced him with the former Strasbourg coach.
Chelsea are currently three points outside the top four, sitting in sixth place on the Premier League table.