The game against Barça in Landover (Washington D.C.) is United's final tour game in America.
Mata returned to training earlier this week but won't be risked any sooner than Sunday in Oslo.
Herrera, meanwhile, was clattered by Real Madrid's Oscar just minutes after coming on as a half-time substitute in the friendly against the European champions in Santa Clara last weekend.
"They cannot play [against Barcelona] but I think they will recover in time to be integrated with the team when we go back to work next Saturday," Mourinho told MUTV.
"They will probably play on Sunday [against Valerenga]."
Herrera is set for another big season as a United player after 2016/17 was his best campaign since joining the club from Athletic Bilbao in 2014.
Mata goes into his fourth full season as a United player as one of the most experienced and senior players in the squad. He's scored 10 goals in each full season to date and fans will be hoping for even more from the popular Spaniard over the next 10 months.