The goalkeeper only signed from Mainz at the start of the summer but was ruled out for an initial eight to 10 week period after breaking a bone in his right hand when coming to punch clear a cross against Chelsea on July 29.
Karius, viewed as the long-term No.1 at Anfield, has trained regularly at Melwood despite his issue, allowing him to maintain match fitness and has continued to train his kicking on the outside pitches.
He could be challenging with Mignolet, who was expected to have to play second-fiddle to Karius if not for the injury, within weeks with the 23-year-old likely to be given the green light to return to full training in two weeks' time, when wiring is removed from his hand.
Liverpool are hopeful that, provided Karius suffers no setbacks between now and then, the 'keeper could be back in contention after the mid-September international break.
Karius targeting speedy return from broken hand
The Belgium international, who has made more penalty saves in the Premier League era than any other Liverpool goalkeeper in denying the fifth of 11 he has faced, will undoubtedly be pushed for his starting spot.
Previous seasons have seen Mignolet struggle for form and yet maintain his place between the sticks due to a lack of real competition or back-up, though Karius' arrival has changed that.
Indeed, Mignolet will hope to use the coming weeks - including this Saturday's trip to Burnley - to prove to manager Jürgen Klopp that he should be ahead of £4.7 million Karius in the pecking order.
Karius rejected the opportunity to represent his country at the 2016 Olympics in Rio in order to complete a full pre-season with the Reds, although his preparations were interrupted by injury.
The former Manchester City youth will be keen to make up for lost time upon his return, with no European football providing a limited number of games for whomever becomes second-choice at the club.