Both wingers sustained knocks in the Red Devils' 3-2 victory over Real Betis in midweek, where Rashford was named in the first XI and struck Man United's first goal from the penalty spot in the 18th minute.
However, the England international had to be withdrawn just after the hour mark on Wednesday, as Betis midfielder Sergi Altimira trod on his ankle, forcing him to gingerly trudge off the field.
Rashford's substitution came just one moment after Antony was brought on to replace Amad Diallo, but the Brazilian could not see out the full 90 minutes, being replaced in the dying embers of the contest.
Man United have already been dealt two crushing blows during their USA tour, with Leny Yoro ruled out for three months with a fractured metatarsal sustained against Arsenal, where Rasmus Hojlund also picked up a hamstring issue that will rule him out for six weeks.
Ten Hag to make 'final assessment' on Rashford, Antony
Speaking to the media in his pre-game press conference, Ten Hag did not rule Antony and Rashford out of Saturday's clash with Liverpool at the Williams-Brice Stadium in South Carolina, but he also insisted that he would not be taking any unnecessary risks ahead of next weekend's Community Shield against Manchester City.
"We have to wait. Of course, we don't go into risk, into the last game of the tour, going into the season next week already, into an important game [against Manchester City]," Ten Hag said.
"We are still within the 24 hours after a game, so the final assessment we have to make and we will see if they are ready for the final game on Saturday against Liverpool."
Should neither Antony nor Rashford make the cut this weekend, Mason Mount and Hannibal Mejbri represent alternative options on the left for Man United in the absence of Argentinian Copa America winner Alejandro Garnacho.
However, Ten Hag also confirmed that the winger and compatriot Lisandro Martinez would both be back in training imminently, adding: "Of course we a plan for every individual where they have to show up and that plan is now running.
"Alejandro will already, tomorrow, start training. Licha will start on Monday so I have it in my mind, and that there is a plan and the need for every player in the off-season. We know every player where they are fitness-wise and next week we have to bring everything together."
Who will start up front for Man United against Liverpool?
Due to Hojlund's severe blow and Joshua Zirkzee being left out of Man United's pre-season tour squad, Jadon Sancho was used in a false nine slot against Real Betis, completing 62 minutes before making way for Ethan Wheatley.
When asked whether Sancho would continue in a central position against the Reds, Ten Hag added: "I think we have to assess next week where we are, and they are in two very different situations.
"Jadon is in a pre-season, in the tour. Joshua had played in the Euros, then had his break and now started training in this week. So next week we have to assess those and we will pick a team that's capable to win the cup in the last game [of pre-season] against Manchester City."
Scott McTominay could also be deployed at the tip of the attack for Man United, who are expected to have Zirkzee available to make his debut in the Community Shield.