The Spanish defender reveals that Jurgen Klopp's side were unwilling to match his £3.2 million release clause but is excited at the prospect of life in the Bundesliga
After two years at Rayo Vallecano, free agent Galvez signed a three-year deal with Werder at the end of the 2013-14 season.
He was reportedly attracting interest from several European clubs, including Manchester United, and has now confirmed that he came close to a deal with Dortmund until they opted against matching his release clause.
"We met in a hotel and talked about a change," the 25-year-old, who made 26 appearances in La Liga last season and scored two goals, told Bild.
"I had an exit clause of €4 million [£3.2m] but Dortmund did not want to pay for it. Then they decided to [go for Greece international] Sokratis Papastathopoulos."
"It would have been a good option but I knew that a new one would come along. Werder is a new option."