The Japanese star signed for the La Liga outfit on loan for the entirety of this season.
The Magpies wanted the 28-year-old sold permanently, but settled on the loan move.
It appears they were quick to back down in negotiations with the Spanish team.
"Newcastle told us, either you reach some figures or Muto does not leave," Eibar sporting director Fran Garagarza told AS.
"We told them that it was impossible.
"A week later the Japanese forward arrived on loan to Eibar for the figures that we initially told them."