Erik ten Hag has called on Manchester United to sign a striker “as soon as possible” to allow enough time to integrate a new recruit into the team, with the manager admitting the club’s failure to do so so far this summer is not ideal.

Having strengthened his midfield with Mason Mount and replaced goalkeeper David de Gea with Andre Onana, Ten Hag is targeting Atlanta’s Rasmus Højlund or Eintracht Frankfurt’s Randal Kolo Muani as his new No 9.

“The only thing I can say is we do everything that’s in our power to get it done,” Ten Hag said. “If it was up to me, as soon as possible, the earlier the better, because we have to integrate him in the team, the way of play. In an ideal situation, he was already here but you do not always get ideal situations as a manager and you have to deal with the situation.”

Marcus Rashford scored 30 goals last season, the first United player to reach that number since Robin van Persie in 2012-13. Ten Hag believes he can be as successful again next year if the 25-year-old has the correct approach.

“When his attitude is right then he will do that, it’s not easy and the team has to play well to put him in the right position,” Ten Hag said. “When the team is playing well, so when we keep the rules and principles in our way of play and Rashford’s attitude is right and he puts himself in the right position, he will finish because has great abilities. When he is in the box, he’s clinical, he’s ruthless, and he scores goals, with his right foot, with left foot and with his head.”

United managed only 58 goals in the Premier League last term, the lowest of all the top-six teams. Ten Hag wants other players to contribute.

“We are underperforming there and we are aware of it so others have to contribute also in that area and therefore we are looking for scoring abilities,” Ten Hag said. “I think in Mason Mount we have a player extra who is capable of scoring goals and creating them, and to play players like Rashford into position to score more goals.”

Anthony Martial trained for the first time on Monday since suffering a hamstring problem in late May. The Frenchman began last season as Ten Hag’s first-choice centre-foward but his tendency to succumb to injuries has thrown his future in doubt.

Ten Hag said: “Today, he was in the team training, so it is really hopeful [he is fit again]. Of course, when you have a player in your squad you have to expect he is available and players have to take responsibility to be available.

“But when he is not, I have to deal with the situation and we have shown we can be successful without that striker. But it’s easier when you have that striker in the team because every club who wins big trophies has scoring abilities in that team.

“We need a good squad and Anthony Martial is a brilliant football player so he will help us score goals. There are other areas like pressing in possession combinations, he’s a great player, so we hope he’s fit and he stays fit.”

Ten Hag will field a United XI that will be mainly made up of junior players against Wrexham at San Diego’s Snapdragon Stadium in Wednesday, with 35-year-old Johnny Evans captaining the side. The following day a senior XI will face Real Madrid in Houston.