The Leicester captain has not featured since scoring in last month's stirring comeback triumph against Sevilla in the last 16 due to a back problem.
The Premier League champions are 1-0 down from the first leg and will be without Morgan's regular centre-back partner Robert Huth through suspension.
Shakespeare told a pre-match news conference on Monday that the 33-year-old is progressing well in his bid to lead the hosts out at a sold-out King Power Stadium.
"The final decision will be made tomorrow," Shakespeare said. "We want to make sure there is no reaction to today's training.
"He has trained the last three training sessions in which the intensity has been greater [in] every one.
"I am pleased with how he has progressed. I would like to find out from the player how his thoughts are.
"But my eyes tell me this morning we both should be fairly pleased how he has come through.
"We're in the tie and it's only 1-0. We need to make sure that we create more, but we also need to be mindful of their players.
"Come tomorrow night we'll be ready both physically and mentally."
A raucous atmosphere and a performance of relentless intensity saw Leicester turn a 2-1 deficit against Sevilla into a 3-2 aggregate win in the previous round and left-back Christian Fuchs is relishing trying to make life difficult for another La Liga opponent.
"I don't think anybody wants to come here. We're the underdogs but we want to take our chance," said the Austria international when he spoke alongside Shakespeare.
"We'll see how the game goes. We’re focused for now but we'll obviously try to give everything.
"We all know Atletico are a great team. It's down to us if we want to advance. There's a lot of pressure always but we're just looking forward to the game."