Lucas spent three seasons under Benitez on Merseyside, making 121 appearances, having been signed by the Spaniard in 2007.
The 30-year-old has outlasted four managers at Liverpool, but is expected to leave this summer, despite Jurgen Klopp affording him 31 outings in 2016/17.
They claim that the Magpies have “enquired about the availability” of the Brazilian, with Benitez earmarking him as an “experienced alternative” to Jack Colback and Isaac Hayden.
It is suggested that, with one year left on his current contract, Lucas would cost around £4 million, which would provide Newcastle with a strong squad option.
Moving to St James’ Park could allow Lucas to prolong his career at the top level, with Benitez spearheading a revival on Tyneside.
“There was an offer from Gremio in January but I wanted to complete 10 years at Liverpool,” he said.
“Now in the window we had a conversation, but nothing official. I do not hide my desire to return to Gremio, but there are several factors.”
Klopp was rightly reluctant to part ways with Lucas in January, and this proved to be a wise move given the amount of times he was required to turn out in both midfield and defence.
But this summer—after Lucas marked a decade with the Reds—is likely to be a different story, with Klopp turning his focus elsewhere.