The influential Jamaican international has featured in both of his side's opening top-flight fixtures in 2017-18, although was not considered for a midweek Carabao Cup second-round victory at Sheffield United due to a back injury suffered in the preceding 2-0 home win over Brighton & Hove Albion.
Leicester faced something of a dearth of central defenders for that fixture at Bramall Lane, with Robert Huth yet to return following ankle surgery and Yohan Benalouane seemingly out of the first-team picture.
Left-back Christian Fuchs eventually lined up alongside Harry Maguire in the middle and 19-year-old academy graduate Josh Knight later came on to make his senior debut.
The Foxes will be pleased to have Morgan back in the fold for a potentially tough trip to Old Trafford, where they will face a confident Jose Mourinho side that have begun the new campaign with successive four-goal triumphs.
"Wes will be involved," Shakespeare told reporters at his pre-match press conference. "He has trained the last couple of days. Hopefully we won't get an adverse reaction."
The good news does not end there, with Jamie Vardy also fit to face United after an ankle knock. Rumoured Chelsea target Danny Drinkwater is back in training following a thigh strain, while summer signing Kelechi Iheanacho is also building match fitness after seeking specialist opinion on a lingering toe complaint. Nampalys Mendy made his first appearance since February on Tuesday night and has not sustained any setback.
"[Iheanacho] is another one who has trained," Shakespeare added. "We have to be mindful about how far we push him. Gradually, he is getting back to fitness."
Huth remains sidelined for Leicester, while new midfielder Vicente Iborra is not expected back from a groin strain until after the forthcoming international break. Maguire, who received his first senior England call-up on Thursday for World Cup qualifiers against Malta and Slovakia, has been kept out of training as a precaution and could be a doubt after being on the receiving end of a heavy challenge against Sheffield United.
Shakespeare remained coy on transfers, claiming not to be aware of any imminent incomings or outgoings and stating that Leicester will continue to deal with all the speculation regarding the likes of Drinkwater, Vardy and Riyad Mahrez before next Thursday's 23.00 BST deadline.
He also hinted that Benalouane could yet have a future in the East Midlands, stating: "I'm not going to shut the door. He's got work to do, which he knows."