According to the Echo, the Spaniard was unhappy that Newcastle failed to match his £65,000 per week Liverpool wage, and was also unimpressed with the length of the deal being offered.
Despite being told he has no future under Klopp, the 30-year-old will now stay with Liverpool until the end of the season when his contract expires.
Liverpool paid Newcastle £7 million for his services in 2011. He was initially a big hit, but his form started to fall away.
He rejected a move to West Brom on deadline day last summer.