According to the Mirror, Ralf Rangnick is a huge fan of the 28-year-old, who is set to become a free agent this summer with negotiations over a deal at Stamford Bridge continuing to stall.
The report adds that the decision to target a new centre-back comes over concerns with Harry Maguire at the back.
The Red Devils captain had struggled for form this season and it has shown in his side's defensive record, with the club having conceded the most goals in the top four and the joint-most in the top six.
Rudiger has emerged as one of the best defenders in the Premier League since Thomas Tuchel succeed Frank Lampard as manager in January 2021.
He helped the club triumph in the Champions League and has been imperious in their five-at-the-back system, helping the Blues become one of the very best defensive outfits in world football.
A host of top teams are monitoring his transfer situation and Real Madrid were seemingly leading the race.
However, reports in Spain earlier in February suggested they have now pulled out of the deal.
Earlier this week, talkSPORT revealed that Wolves' Max Kilman is a target for Chelsea as they look to bolster their defence ahead of the 2022/23 campaign.
The 24-year-old has been a standout performer for the Wanderers in their impressive campaign under Bruno Lage.
Sevilla's Jules Kounde, whose move to Stamford Bridge fell through in the summer due to a breakdown in negotiations, is also believed to be one of the top priorities.
The Blues wanted the centre-back last summer but were not prepared to pay his £68m buyout clause and the Spanish club were reluctant to sell even with now-West Ham ace Kurt Zouma offered as part of the negotiations to bring down the fee.
It's believed the Sevilla will allow the player to leave for a fee of £45m- £50m next summer, less than what they demanded before - but Man United are also keen to sign the 23-year-old.
Another option is Juventus ace Matthijs de Ligt, whose massive £103m release clause will become active at the end of the season.
The Dutchman joined the Italian giants from Ajax for £67.5m in 2019 but hasn't been the hit many thought he'd be and the club are believed to be considering offers.
On Maguire, a former Manchester United star recently said the Red Devils are 'stronger without' the England international in their team, with Kleberson urging the club to replace him.
"Manchester United look far more assured with Raphael Varane and Victor Lindelof at the back, rather than Harry Maguire," said the Brazilian.
"Manchester United need to make some signings at the centre back position to replace Harry Maguire.
"He's a great player and leader, but there are too many moments that he just doesn't perform, particularly when he's one-on-one, or up against pacey players. He needs help defending.
"They need someone faster, stronger in the air, that can anticipate what will happen and that will be able to stop counter attacks."