Owen has been out with a hamstring injury that he picked up in the League Cup final against Aston Villa on February 28.
“We [the Manchester United squad] are not in [training] until July 5, that’s when everyone’s in, but I have been working through June because it would be nice if I could start and do everything with the team straight away,” he told Sky Sports News.
“It’s looking so far that I will be able to do that.
“Hopefully I won’t miss any pre-season training, as it’s always nice to get a full pre-season in. I am working hard at the minute.”