According to the Daily Star, the Reds want to bring in the German either on loan or permanently to solve their current goalkeeping nightmare.
Current number one Simon Mignolet has been heavily criticised this season for a series of errors, leading to him being benched at the end of 2014. Liverpool want ter Stegen to become their new number one for the forseeable future.
It is thought that Barcelona have similar intentions for 22-year-old ter Stegen, who has been vocal about his lack of playing time recently.
“The situation is difficult,” said ter Stegen. “I’d be lying if I said I didn’t care and it isn’t easy being a spectator.
“I want to be the No. 1 so it’s something I will fight for. For now, the manager counts on me for the Cup and Champions League, but I’d like to play in the league. I want La Liga, even if Bravo is doing a good job.”
The young stopper only joined Barca in the summer from Borussia Monchengladbach for £9.7 million and has performed well in his recent Copa del Rey outings.