Embleton missed the 1-0 friendly win over Harrogate Town at the Stadium of Light with a thigh injury but Parkinson hopes to have him back running Monday.
Sunderland start the 2020-21 campaign with the visit of Hull City in the Carabao Cup on Saturday, with the League One season starting the following weekend.
Parkinson also confirmed the decision to substitute Jordan Willis and Josh Scowen was a precautionary one.
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Neither look like serious injuries.
“Jordan just felt his groin tighten during a clearance, and we obviously weren’t going to take any risks with him,” Parkinson said.
“Josh has just picked up a bruised foot/ankle in a challenge, but it doesn’t look too bad at the moment.
“Elliot [Embleton] hasn’t trained yet but he should be back running on Monday.”
Meanwhile, former Sunderland No1 Jon McLaughlin has been speaking about his move to Rangers and how the chance to work alongside Allan McGregor will help him reach new levels.
McLaughlin said: “Allan has been great to me but all the keepers get on well and we have a good relationship. It has been an easy transition coming here.
"One of the big reasons of coming here was the experience Allan has, to work with someone like him day in and day out can only make me a better goalkeeper.
"He is back from his injury and we have been getting on well so we will see how we get on from here.”