Sir Alex Ferguson is thought to be willing to offload the striker, who has fallen behind Danny Welbeck, Wayne Rooney and Robin Van Persie in the pecking order, and Real Madrid boss Jose Mourinho is believed to be interested.
But rather than a cash purchase, Manchester United reportedly want to swap Hernandez for one of Real Madrid's stars.
United have previously been credited with an interest in Raul Albiol and Raphael Varane, both centre-backs, but according to the Daily Star, Ferguson's ideal target is Brazil star Kaka.
The 2007 Ballon d'Or winner has been a long-term Manchester United target, and reportedly came close to joining the Old Trafford side last summer.
The Brazil international has fallen out of favour under Jose Mourinho at Real Madrid, and earlier this summer the Portuguese boss admitted Kaka could leave for first-team football.
He came close to returning to AC Milan, but a deal fell through, while Spurs were also thought to be keen on the talented playmaker.
But Manchester United now seem to have moved to the front of the queue for the 30-year-old - who remains one of the most high profile, and highly-rated, players in world football.