The Mexican international has fallen out of favour at Old Trafford, and has also interested Inter Milan and Valencia this summer with the striker seemingly surplus to requirements.
United have been linked with a £27m transfer for the England left-back Shaw, who is currently in Miami as Roy Hodgson's side prepare for the World Cup finals, which start next week.
Including Hernandez in the deal could see the transfer completed sooner, with the Saints in desperate need of forwards. Jay Rodriguez will be out until the winter after rupturing his cruciate knee ligament, Dani Osvaldo is expecting to move back to Italy, and Rickie Lambert joined Liverpool earlier this week.
Adam Lallana could join Lambert at Liverpool. The England midfielder made his desire to leave the Saints clear this week, but the club are holding out for £30m for the player.