Garnacho, a highly-rated young player, has been linked with a move away from United, while Antony has impressed in his loan spell at Real Betis since joining in January.
Bayer are reportedly willing to meet Manchester United's asking price for both players, thanks to the imminent sale of Florian Wirtz, which will give them the necessary funds to complete the transfers.
Other clubs, including Napoli, are also interested in Garnacho, while Betis are keen to sign Antony permanently.
