Morgan, the Leicester captain and centre-back, has been sidelined with a back injury since mid-March and was again missing from the squad that drew 2-2 at Crystal Palace.
But with Robert Huth suspended for the Atletico return -- with the English champions trailing 1-0 -- Shakespeare's options in central defence are stretched.
The Leicester manager revealed Morgan had successfully come through a training session on Friday, raising hopes the 33-year-old can face the La Liga side.
"It looked better yesterday," said Shakespeare, speaking after the match.
"He trained with the group for the whole session. I hope he joins in with the rest of the group tomorrow.
"It's a big ask for him because it's a difficult injury to get over, in terms of the power and spring for a centre-back.
"But we'll give him every opportunity and, with the medical staff, we'll see what their feelings are and we'll make a decision."
Shakespeare was also relieved to discover Yohan Benalouane had not suffered a significant injury despite being forced out of the Palace meeting late on in the game.
"I'm assured it was just cramp," said Shakespeare. "Cramp can turn into a pull, so it was just a precaution. He's walking at the moment.
"We'll get it looked at. They're in tomorrow for a recovery session and we'll assess it then," added the 53-year-old.
Leicester appeared set to head into the Atletico match on the back of a victory that would have drawn a line under any lingering relegation fears.
- 'Great point for us' -
But having established a two-goal lead through a sixth minute Robert Huth header and Jamie Vardy’s 52nd minute strike, they allowed Palace to recover with Yohan Cabaye reducing the deficit in the 54th minute before Christian Benteke levelled in the 70th minute.
"There is a tinge of disappointment, especially when you go two up away from home," said Shakespeare.
"Their first goal was all important for them, two minutes from our second.
"We could have seen it out if we'd stayed in the lead a bit longer, but they asked a lot of questions of us with their aerial threat. We should be pleased with a point, probably."
Palace manager Sam Allardyce was relieved his side avoided defeat having been so impressive in beating Arsenal 3-0 last Monday, although he was frustrated at the way they conceded the opening goal following Christian Fuchs' long throw.
"We practised it here on the pitch yesterday. Unfortunately for me, players forgot," said Allardyce.
"It's that simple. They weren't anywhere near where we put them, sadly which is why he ran in with a free header and scored.
“Those are the basics, and that's why I continue to bombard the players to get the basics right."
The draw moved Palace seven points clear of third from bottom Swansea leaving Allardyce very satisfied.
"It's a great point for us," said Allardyce. "On reflection, when you finish a game with a point having been 2-0 down, you have to be incredibly satisfied with that point however precious it might be moving forward."