The Toffees announced yesterday that they had agreed a fee with their Dutch counterparts for the 23-year-old.
However, reports over the last few hours had claimed that the deal was being held up because the Everton medical staff were concerned with a knee problem that had shown up on Fer's medical tests.
Despite attempts to renegotiate a fee with Twente which would have been based upon appearances, the Premier League outfit have now opted to pull out of the deal.
"It's a real shame. We were really excited about the prospect of Leroy Fer coming to Goodison," the club's chief executive Robert Elstone told Sky Sports News. "We thought only 24 hours ago that we had a very talented Dutch international coming here.
"The transfer didn't go smoothly in the end and there were some issues. As our fans would expect, we have to put the club first. Our track record shows that we do that very well.
"Unfortunately it didn't work out and that is because we have to be very careful about where we spend our money."
Elstone went on to confirm that the club have now turned their attention to alternative options.