United will take on Villa in a pre-season friendly on Saturday ahead of the new Premier League season.
The Red Devils beat Dean Smith's side 3-0 at Villa Park when they last met, with the clubs drawing 2-2 at Old Trafford earlier in the campaign.
And, speaking ahead of the showdown, Solskjaer has revealed Shaw is available again - and that Axel Tuanzebe is edging closer to a return to action as well.
“For me, Luke is looking really good in training. He has come back, looking strong, and will play in the friendly against Villa," he told the club's official website.
“Then Axel is getting closer as well. In a few weeks' time, I guess he will be with us training full-time and hopefully we'll be able to give him games quickly."