However, it remains to be seen whether Paul Pogba and Romelu Lukaku, will travel with their futures in doubt.
United are not heavily affected by Copa America and the African Cup of Nations, with only Chilean forward Alexis Sanchez on national team duty.
This means Solskjaer will be able to take a full complement of players to Australia for the first leg of their tour.
“Summer has been kind to us in that respect – so we’ll travel to Perth with the full first team squad.
“Everyone should be available to be picked – hopefully they’re fit when they come back – so the first team is going to be there,” Solskjaer said via the club’s Facebook page.
United will begin their pre-season against Australian A-League premiers Perth Glory on July 13 at Optus Stadium, before taking on Leeds United at the same venue four days later.
“To play against (A-League premiers) Perth Glory is always a good reference point on how the leagues compare.
“Games against Leeds United have always been huge for us. I’ve played in quite a few – both on-and-off the pitch there is some rivalry,” Solskjaer said.
Following the two matches Down Under, the Red Devils face Inter in Singapore on July 20, before wrapping up their tour against Tottenham in Shanghai on July 25.
