According to The Daily Mirror, Mexican international Hernandez was Saints manager Ronaldo Koeman's top transfer target at St Mary's, but the 26-year-old - who has been told he is free to depart Old Trafford - has turned down the possibility of moving to the South Coast as he looks to join a club set to be involved in European competition this season.
Indeed, the same source goes on to suggest that, after receiving such a rejection from Hernandez, Southampton have quickly progressed to agree an eye-catching £12 million fee with Premier League rivals Hull City for the transfer of Republic of Ireland forward Shane Long.
Hernandez leaving Old Trafford?
Last season was an extremely difficult one for Hernandez. Having carved out an effective reputation as one of the top-flight's finest impact substitutes, he evidently found it hard to make much of an impression during the doomed reign of David Moyes.
£15 million-rated Hernandez scored just four goals in 24 appearances in 2013/14 and the former Guadalajara frontman now looks to be surplus to requirements at Old Trafford following the arrival of the ruthless Louis van Gaal.
Hernandez - who moved to Manchester United from his homeland back in 2010 - is among seven first-team players who have reportedly been told to move on this summer, with the likes of Wilfried Zaha, Nani, Anderson and Rafael all seemingly deemed expendable by Van Gaal.
With a transfer to Southampton now seemingly out of the question, interest in Hernandez could intensify.
Reigning Serie A champions Juventus have also been credited with a strong interest in the player, and that surely is a move that could appeal given the Old Lady's strong domestic record and participation in the Champions League.
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For Southampton boss Koeman, missing out on his primary target should come as a disappointment, but in former Reading favourite Long he will be getting a likeable character and a tireless worker who should be capable of thriving alongside Italian Graziano Pellè.
While Long's impressive speed and deceptive strength should be well received by Saints fans, they can certainly be forgiven for harbouring legitimate concerns regarding that extravagant £12 million fee - particularly since Hull spent approximately £7 million to take him to the KC Stadium from West Brom just seven months ago.
Southampton will, however, simply have to become accustomed to paying inflated fees for the remainder of the current transfer window.
With the club having pocketed huge sums from the sales of a number of their best players in recent months, rivals will be well aware of their financial reserves and will seek to receive as much compensation as possible during such transactions.