The Spaniard was handed a rare start against Exeter on Friday.
The Spanish defender was handed a start at centre back for their FA Cup third round clash with Exeter on Friday evening.
That was a rare appearance for the Reds for him, as he last appeared at the same time last year for the club.
He is far down the pecking order at Anfield; with Alberto Moreno the first choice left back and youngsters such as Joe Gomez and Brad Smith currently ahead of him when fit.
And former Liverpool midfielder Murphy has admitted his surprise that he hasn’t pushed Moreno more this season.
“I’ve always thought he was a talented fullback, and a good footballer,” he told BBC Sport.
“They’ve only got Moreno really who has played in that position this season, I thought he could have pushed him a bit more.”
“Obviously he hasn’t been training enough, or he isn’t fit enough.”
While Enrique has found himself far down the pecking order this season and last, this part of the season could see him finally getting extended game time.
The Reds have been hit by an injury crisis in January, with a number of first team stars, especially defenders, currently on the treatment table for various injuries.
That might see Jurgen Klopp make moves in the transfer market, but until he can potentially secure new singings, he may be forced to rely on the likes of Enrique during what is a gruelling January schedule.