Klopp has spoken highly of the player previously. Last December, he said of Gross: “I have known him since he was a kid. He is a fantastic player that has made another big step physical wise.
"He has a nice right foot, is good at set-pieces and a nice shooter.”
The 27-year-old bagged the Brighton Player of the Year award in his first season in English football and was rewarded with a new four-year contract in June.
Due to an ankle injury at the beginning of the new campaign, Gross has only made eight league appearances so far, as Brighton currently occupy 12th place in the Premier League table.
While Liverpool were strongly linked with Lyon’s star man Nabil Fekir during the summer and beyond, Klopp and the recruitment team are believed to be looking elsewhere to strengthen in upcoming windows.
Brighton host the table toppers Liverpool on the 12 January 2019, with the possibility that Gross could make an early return to the Amex Stadium should the deal go through.