The France midfielder, 26, has been absent from training this week with boss Ole Gunnar Solskjaer's permission, BBC Sport reported.
There has been speculation about his long-term future this summer and in June, he said "now could be a good time to find a new challenge".
On Friday, agent Mino Raiola stated again that Pogba wants to leave United.
Summer signings Aaron Wan-Bissaka and Daniel James are also both in the traveling squad, as is Romelu Lukaku, who has been linked with a move to Inter Milan.
Brazilian midfielder Fred and defender Matteo Darmian were both excused from Sunday's trip for personal reasons but are expected to link up with the United squad at some point before it returns to England on July 26.
Alexis Sanchez only finished Copa America duty with Chile last night and wouldn't have been involved, even without the hamstring injury he sustained in the third-place playoff defeat by Argentina.
United is due to land in Perth on Monday.
The English giant plays Perth Glory on July 13 and Leeds United on July 17 before flying to Singapore for a game against Inter Milan on July 20. The Red Devils finish their trip with a game against Tottenham in Shanghai on July 25.