Johnson pleaded guilty to one count of sexual activity with a child and one count of grooming at Bradford Crown Court on Wednesday.
He continues to deny two charges of sexual activity with a girl under the age of 16 and will be on trial from Friday.
Following his arrest and subsequent bail last March, Sunderland suspended Johnson before clearing him to return to first-team duties when his bail was extended by Durham Police.
But Allardyce will not be calling on Johnson for the visit of Louis van Gaal's men and had no update to offer on what would happen with his player for the remainder of the season.
When asked if he would be in the squad, Allardyce replied: "No. Johnson won't be available for this weekend.
"I don't know [about the following games]. We will see how it goes beyond that."
Sunderland-born Johnson, who has 12 England caps to his name, moved to the Stadium of Light from Manchester City in 2012.
He was on the scoresheet last time out - in what could potentially be his final appearance for the club - firing a free-kick past Simon Mignolet in a come-from-behind 2-2 draw against Liverpool at Anfield.