But Klopp knows more is required if the Reds are to finally secure a first-ever Premier League title.
Don Balon say that, initially, Vazquez was determined to stay at Real.
However, Klopp’s perseverance means a move to Liverpool looks increasingly likely for the summer.
Real could, though, try and use the player in a deal for Salah.
The La Liga giants are determined to make the Egypt international the perfect partner for Cristiano Ronaldo.
But, speaking last month, Klopp insisted Salah would be staying at Liverpool.
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Liverpool transfer news: Jurgen Klopp has tempted Lucas Vazquez into leaving Real Madrid
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"It's not the situation where I would even think about it," said Klopp, when asked if Salah could leave.
"Mo Salah came in nine months ago to make the next step in his career and he did it.
“To come to Liverpool, he had different options and he wanted to come here, so if we always start talking after a year 'will he leave' - I don't think about it.
"I'm confident. I think, no I don't think, I know he will be here.
"We don't want change all the time. We have a big chance here to create something for the future. My impression at the moment is they are all excited about being in this group."