Koeman is keen to take the Mexican to St Mary's, but doesn't want to be waiting while Chicharito weighs up his options. Saints are in contact with the player's camp and want an answer in the next 48 hours or they'll move onto other striker targets.
Dutch sources say United have put Hernandez up sale and clubs across Europe are aware of the terms.
United are seeking €9.5 million cash up front to sell immediately, or €11.5 million to be paid in installments over 12 months.
They are also willing to send Chicharito away on-loan with the option to sell next June.
For the big stories and the banter follow us on Twitter: @tribalfootball