BILD report that United remain undecided over whether to commit the substantial fee needed to prise the 28-year-old away from RB Leipzig, with question marks over his age and whether the funds would be better invested in a younger prospect.
Raum, who turned 28 in April, has 39 caps for Germany and has made more than 100 Bundesliga appearances, along with 19 outings in the Champions League.
He emerged as an option after United were unable to convince Newcastle United to sell Lewis Hall, their long-standing top target for the position, and have also looked at alternatives including Barcelona's Alejandro Balde and Club Brugge's Joaquin Seys as Luke Shaw's persistent injury problems leave the club short of cover at left-back.
Away from that decision, United have completed the sale of midfielder Toby Collyer to Championship side West Brom, where he spent a loan spell last season. An initial fee of £3m has been agreed for the 22-year-old, rising to £7.6m with add-ons, and United have retained a 40 per cent sell-on clause as part of the deal.
Collyer had been weighing up a return to West Brom or a switch to fellow Championship club Hull, where he also spent time on loan during 2025-26. West Brom initially looked to be favourites for his signature, before Hull appeared to move ahead in the race. In the end, Baggies boss James Morrison persuaded Collyer to choose the Hawthorns.
Collyer's game time at West Brom last season was restricted by injury, but he still did enough to convince Morrison of his qualities during the first half of the campaign. The prospect of regular first-team football is understood to have been the decisive factor in his decision to snub Hull City, who had also made a serious push to sign him following his impact after joining them for the second half of last season.
Collyer, who joined United from Brighton's academy in 2022, made 13 first-team appearances for the club during the 2024-25 campaign but had fallen well down the pecking order in central midfield this summer, with Manchester United having already invested heavily in the position through the signings of Carlos Baleba, Andrey Santos and Youri Tielemans.