The two youngsters are highly-rated within the club and have featured in both thrilling League Cup victories, which has set the Reds up for a quarter-final clash with Aston Villa in December.
Their involvement beyond the domestic cup action has been limited, however, and the Reds and now weighing up temporary departures for the pair in the January transfer window.
As ever, Liverpool will first seek assurances over playing time before sanctioning a move for the 19-year-old who is yet to make his Premier League bow.
While he has been provided with few opportunities at senior level thus far at Anfield, he has talent in abundance and is said to have attracted interest from Aston Villa, Crystal Palace and Championship side Swansea – who are pushing for promotion this season.
But with the Reds holding high hopes for the Irishman, who was the hero in the penalty shootout win against Arsenal, they are prepared to sanction a move to see him gain experience instead of solely acting as a travelling member of the senior side.
Preston North End are reported suitors for Kelleher, but it remains to be seen whether the Championship outfit would be a good fit as former Norwich stopper Declan Rudd is currently the undisputed first choice.