FSG were in negotiations with Getafe owner Angel Torres about a deal for the Spanish club.
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It's been claimed FSG were willing to pay £100m for the Madrid-based outfit, though Torres priced the club closer to £160m.
Marca says FSG have now dropped plans of buying out Torres.
LaLiga's salary cap rules have put off the Americans as it would work against FSG plans of quickly revamping the club's squad.
There were also concerns about the average age of the Getafe squad - 28 - which would work against FSG's youth model.