Enrique was told to train away from the first team under Brendan Rodgers earlier on in the season.
Enrique trained away from the main group in pre-season and was told to find a new over the summer by Brendan Rodgers, prior to the Northern Irishman's dismissal in October, and he has not played a game for Liverpool since January.
It is an area where Liverpool are pretty short on cover, though, and could do with all the players they can get. If the 30-year-old can put his recent injury problems behind him, then he may well prove useful as the Reds will still look to compete on four fronts, while also having to deal with the hectic Christmas schedule that is on the horizon.
Some will question whether he is good enough for Liverpool at the moment, but that remains to be seen, given the level of improvement that Klopp could get out of Enrique.
Then there is the sole reliance on Alberto Moreno. He may well be showing his own signs of improvement under Klopp, but there has to be a time when he is given a breather so that he is fresh enough for the second half of the campaign.
It really is the last chance for Enrique to impress on Merseyside, as his contract expires at the end of the season, meaning that failing to catch the eye could not only harm his chances of continuing his career at Anfield but also getting a good deal elsewhere should he leave the club in the summer.
Given Liverpool's long list of injuries, they should be glad to have another player back within their first team ranks, even though he is not registered for the Europa League squad at the present time.