After disappointing Premier League campaigns in their own right, United and Chelsea are in the market for fresh faces as they bid to close the gap to Manchester City and Liverpool.
However, despite the desire to acquire new additions, neither club have made a signing heading into July, something which is likely to lead to a busy two months.
Bringing in a new central defender is a priority for each of Erik ten Hag and Thomas Tuchel, and it appears that they are assessing whether to rival each other for the same target.
According to Nice-matin, the two English giants are involved in the race to sign the highly-regarded Badiashile from Monaco.
The Ligue 1 outfit have already witnessed Aurelien Tchouameni depart Stade Louis II for Real Madrid for a fee which could rise to in excess of £80m.
Centre-back Strahinja Pavlovic has also departed for Red Bull Salzburg, already leaving Philippe Clement one centre-back down ahead of the new campaign.
Nevertheless, while club and head coach would prefer to retain the services of Badiashile, the 21-year-old has just two years remaining on his contract.
That detail effectively leaves the France Under-21 international on the market to interested clubs, Monaco potentially not wanting to run the risk of the player's contract entering its final 12 months.
With Monaco involved in the Champions League qualifiers, Clement may want to retain Badiashile's services until it is determined whether the club will compete in the group stages of European football's premier competition.
That said, interest from elsewhere is not going to go away, and the report suggests that several other clubs are ready to mount an approach for the emerging talent.
Newcastle United are suggested as admirers of Badiashile, even though the Magpies have just shelled out £37m on signing Lille's Sven Botman.
Atletico Madrid and Sevilla are also said to be ready to make their own bids, the latter in the market for a replacement for Diego Carlos who has signed for Aston Villa.
Sevilla may also generate at least £50m through the sale of Jules Kounde over the coming weeks, funds which theoretically could be used to win the race for Badiashile.