Mignolet, 25, who arrived Anfield from Sunderland in summer made a good start, but has struggled in which he made recent expensive errors including one against Manchester City at Etihad Stadium.
However, Brendan Rodgers is keen to bring newly talented stopper at Anfield in order to challenge him for a first choice.
Current back-up Brad Jones is not capable enough to do so, and Rodgers believes Darlow has something who can give a tough competition between the sticks to Mignolet.
The 22-year-old, Darlow has been in impressive form this campaign, and considered as one of the hottest property in the Championship.
Wigan’s Lee Nicholls is also under Reds radar, but it is believed that Darlow would be a better option.