Chris Coleman reveals massive injury blow with four players out for the season
Donald Love will also be missing for the final three games, alongside Jonny Williams.
Goalkeeper Robbin Ruiter had already been ruled for the rest of the campaign with a finger injury.
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Hide AdGooch had impressed on the right-wing after returning to the fold against Derby County on Good Friday, while Asoro has broken into the set-up this season and caused problems with his pace.
“Gooch and Asoro are both out for the season,” Coleman said.
“Goochy got a kick on the bottom of his quad and knee and that will keep him out for the season, and Jonny Williams probably isn’t going to make it back before the end of the campaign.
“Donald Love is also out for the season.
“In the last minute at Reading he got a booking after coming across the guy, and he’s hurt the ligaments in his knee.
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Hide Ad“Joel’s is a hamstring which happened yesterday right at the end of training, and realistically that’s going to be a two to three-week injury," he added.
“John O’Shea has a chance to train on Thursday and Oviedo will train on Thursday, as will George Honeyman who had sickness today, but he’s like a Duracell battery so he should be okay.”
Sunderland face Burton Albion on Saturday before finishing their campaign with games against high-flying Fulham and Wolves.
The 2-2 draw with Reading on Saturday leaves them six points adrift of safety.