Spaniard Herrera has been out of action since mid December through injury but is closing in on a return, while Januzaj is also back in action after illness.
"Herrera trained today [Tuesday] for the first time with us but, yes, they don't have match rhythm," boss Louis van Gaal told a media conference.
"Januzaj has also trained two training sessions with us, but he was ill and you have to recover from your illness, not from your tiredness.
"Maybe it's worse to recover from illness."
The duo's return is a boost for United, who have been hit by absences in key positions in recent weeks.
However, when asked if he would have more players available for the Stoke clash on New Year's Day than he did for the 0-0 draw with Tottenham on Sunday, the United manager replied: "No".
"You have seen that [Chris] Smalling, [Luke] Shaw and Rafael Da Silva are coming back [after featuring as second-half substitutes against Spurs]," he added.
"These are the first signs that we already predicted two weeks ago, that the players shall come back but they are not back with 100 per cent match rhythm, and now we have to play.
"It’s a problem for me to come through this two weeks around Christmas and New Year, all these matches. That is difficult now."
Meanwhile, Van Gaal has heaped praise on United's fans as he continues to push the club up the Premier League table.
The Dutchman moved to Old Trafford in the close-season following the disappointing campaign under David Moyes in 2013-14.
After a shaky start to his tenure, which included an embarrassing 4-0 League Cup defeat to third-tier MK Dons, Van Gaal and United have started to turn things around.
The 13-time Premier League champions have hit their stride in recent weeks, with a run of seven wins and two draws from their last nine outings seeing them climb to third.
And ahead of the trip to Stoke, Van Gaal has thanked United's fans for their unwavering support.
"I think the fans [have been] fantastic because we were in a moment with 11 matches and 13 points - that is not good, I think more weak than good," he said.
"In spite of that, the fans have supported us always and in the right way. I want to thank the fans for that.
"I think the main reason they have supported us is because of the fighting spirit of my team.
"We were not always ahead in matches but they have fought to the end and a lot of times with good success, so I think we can be satisfied about the points now - 36 points."
