Erik ten Hag has not ruled out signing another centre-back before the transfer window closes.
Manchester United spent £59million on signing 18-year-old defender Leny Yoro from Lille, but Ten Hag said there could be another addition before the August 30 deadline.
United retain interest in Jarrad Branthwaite, but have refused to meet Everton's £70m valuation, with Bayern Munich's Matthijs De Ligt a more realistic target at £42m.
Ten Hag said: "I think we are occupied [in that position] but we work continually. The good thing is we already signed two players, but it belongs to a club like Manchester United that you are still looking - if the opportunity is there - for better and we still have time, until August 30."
United suffered more than 60 separate injuries last season, predominantly in defence, with Ten Hag admitting the expanded European schedule is likely to see more players sidelined with the extra fixture burden.
"We already made our decisions [to address the injury situation]," said Ten Hag. "We appointed a new club doctor last season and he started late in the season, but now he can start fresh and be in the lead. We also appointed a new head physio, so we made changes. We also changed strategies in medical and performance to improve, but that is normal.
"Now in football, the developments are so fast, every time you have to innovate and if you want to be the best, you also need the best in those departments.
"There were so many reasons [for the injuries last season]. The amount of games, the fixture list, the load on the players, the pressure on the players is so high and we're not the only team with so many injuries.
"We were not even the worst. Our bad luck was that we had them at the end of the season, in the back four, and it cost us a lot of points.
"The load and pressure on players is immense, with the new model in Europe. It's survival of the fittest. The players have to work in the right way because the standards are so high and you have to fulfil them and reach the highest standards, not only on game day, but every day."
Join our new WhatsApp community and receive your daily dose of Mirror Football content. We also treat our community members to special offers, promotions, and adverts from us and our partners. If you don't like our community, you can check out any time you like. If you're curious, you can read our Privacy Notice.
You may also like
Late Queen's right-hand woman almost scuppered touching funeral moment but eventually caved
Snooker star eyeing £500k Saudi jackpot so he 'doesn't have to play until Christmas'
Oasis' disabled fans make shocking claim about Ticketmaster's sales system
RG Kar rape case: Sanjay Roy's judicial custody extended by another 14 days