The France international struggled for regular starts in the first half of the 2021-22 campaign, which saw him move to Sevilla on loan during the January transfer window.
Martial found it difficult to make his mark for the Spanish outfit, though, managing only one goal and one assist in 12 appearances in all competitions.
Earlier this summer, it had been thought that the 26-year-old would be on his way out of Old Trafford, but Edinson Cavani has departed on a free transfer, while there is speculation surrounding Cristiano Ronaldo's future.
As a result, it is believed that the decision has been made for Martial to stay with the club this summer.
The forward has made an impressive start to pre-season, finding the back of the net against Liverpool on Tuesday before registering once again in Friday's 4-1 success over Melbourne Victory.
Ten Hag has seemingly confirmed that Martial will be remaining at the club for the 2022-23 campaign, and the head coach has challenged the former Monaco youngster to have "the right focus".
"I'm sure he can come back even better," Ten Hag told reporters. "I think when he has the right focus and the right motivation and he works hard he will have production because he is a good player. I say when he has the right focus and every day delivers much then he will have production and it's up to him."
Martial still has two years left to run on his contract with the Red Devils, and he has been training with the club since the start of pre-season on June 27.
He has represented Man United on 269 occasions since his arrival from Monaco in 2015, finding the back of the net 79 times in all competitions, in addition to contributing 50 assists.
Martial impressed as a centre-forward during the 2019-20 campaign, scoring 23 goals and registering 12 assists in 48 outings, but he only scored once in the league in the first half of last term before joining Sevilla.
Ten Hag also provided updates on the fitness of David de Gea and Raphael Varane, with neither player in the squad for the clash against Victory.
De Gea picked up a small issue against Liverpool on Tuesday and was not risked for the team's second match of the summer, while "something small" also kept Varane out of the contest.
"You saw against Liverpool he [De Gea] fell out but he trains already, he is back on the training pitch, no big worry. Raphael Varane also training but something small and I expect him back on the training pitch," Ten Hag added.
Man United will take on Crystal Palace in their next pre-season match on Tuesday before facing Aston Villa in their final game of their Australia tour next weekend.