Costa made just seven league outings from February onwards after suffering niggling setbacks to a long-standing injury, but Mourinho has revealed even scans do not show any damage.
"Costa is not ready. It is not a good feeling for him, it is not a good feeling for me," Mourinho told reporters. "I have to be honest and say that it is a bit of a concern. A player that didn't finish the season and [then] doesn't start the season obviously doesn't make me happy.
"The boy is trying hard but he has a problem against Barcelona [last Tuesday]. The scans show there is no injury so next day he trains, but the next day he is not comfortable. Then, 24 hours before the [Community Shield], we don't know if he plays or doesn't play.
Mourinho added: "I won’t risk my reputation again. You asked me before last weekend and I told you he was ready to play. He wasn’t. I don’t know. I don’t risk saying yes, and I don’t risk saying no. On Friday at the next press conference I think I will tell you again that I don’t know."
Chelsea host Swansea City to Stamford Bridge on Saturday as they start the defence of their league crown, with Radamel Falcao or Loic Remy expected to lead the attack.