The Red Devils have boosted their left-back options with the arrival of Tyrell Malacia from Feyenoord, while Ajax's Lisandro Martinez is believed to be the club's main target in central defence.
Man United also continue to work on a deal for Barcelona's Frenkie de Jong, while Christian Eriksen is expected to soon be confirmed as the club's latest arrival.
There is also allegedly still interest in Ajax attacker Antony, with the 20-time English champions looking to bring at least five players to the club before the end of the month.
According to the Manchester Evening News, Ten Hag is also keen to sign a new right-back to provide competition for Diogo Dalot during the 2022-23 campaign.
The Man United boss has allegedly made Aaron Wan-Bissaka surplus to requirements, with the Englishman largely failing to impress since arriving from Crystal Palace in 2019.
Wan-Bissaka was the team's first-choice right-back at the start of last season, but he largely had to play second fiddle to Dalot in the second half of the campaign under Ralf Rangnick.
Dalot ended last season with 30 appearances to his name, while Wan-Bissaka played on 26 occasions, and the latter is said to be available for purchase in the current market.
Speaking to 101 Great Goals, Dalot's agent Carlo Goncalves recently said: "He is very happy at Manchester United. The season went well for him personally, but obviously, it didn't go well for Manchester United given the club's expectations. But we are expecting Diogo to stay for next season, for sure."
Brandon Williams and Alex Telles are also said to be surplus to requirements at Old Trafford this summer, with Ten Hag keen to overhaul a defence that struggled last term.
Inter Milan's Denzel Dumfries was strongly linked with a move to Man United last month, with the Red Devils thought to be exploring the possibility of signing him in the current market.
The 26-year-old was a key player for Inter during the 2021-22 campaign, contributing five goals and seven assists in 45 appearances in all competitions.
A recent report claimed that a fee in the region of €30m (£26m) could be enough to sign the Netherlands international, who arrived at San Siro from PSV Eindhoven last summer.
Dumfries scored five goals and provided five assists in 33 Serie A appearances during the 2021-22 campaign, while he also featured on seven occasions in the Champions League.
Man United are also believed to be looking for another central midfielder alongside De Jong, with Leicester City's Youri Tielemans still being strongly linked with a switch to the club.