The 25-year-old was one of seven new signings who arrived in the summer but while the likes of Charlie Adam, Jordan Henderson, Stewart Downing and even Craig Bellamy have grabbed all the attention Enrique has gone somewhat unnoticed.
His contribution, however, deserves more than a fleeting mention as the Spaniard has played every minute of all seven Barclays Premier League matches.
The seamless way he has slotted in at left-back, a problem position at Liverpool for some years, probably partially explains why he has not been singled out as others have.
But that has not slipped the attention of those within the walls of the club's Melwood training ground with Clarke full of praise for the former Newcastle defender.
"He wants to improve. I know he is desperate to be part of the Spanish squad in future," said the Scot.
"If he continues the work he's doing and manages to improve then I am sure he will make the squad, no problem."
How Enrique has so far failed to catch the attention of national team boss Vicente Del Bosque remains a mystery.
Spain's first-choice left-back used to be Joan Capdevila but his summer move to Benfica has turned sour very quickly and he has been frozen out. His age is also starting to count against him as he will be 34 in February.
Del Bosque has recently used Real Madrid's former Liverpool right-back Alvaro Arbeloa on the left while Atletico Madrid centre-back Alvaro Dominguez has also been tried in the position.
For the Euro 2012 qualifiers Del Bosque has selected uncapped Valencia left-back Jordi Alba, meaning Enrique was left behind to train at Melwood with the half-dozen non-internationals from the first team.
Enrique has brought more balance to the side and his partnership with Downing is developing well, while he has provided assists for Luis Suarez and Andy Carroll in the last two matches.
"As an ex-full-back myself I can appreciate the work he's doing for the team - both in attack and defence," Clarke told liverpoolfc.tv.
"I'm sure he'd be the first to admit he's got lots of things he can work on to improve but from what we've seen so far from him he should be pleased with himself and the contribution he's made.
"We've been impressed by the way he's gone about his business day-to-day in training and I think that is when you get to know your players best, by working with them every day."
The international break has also given the Liverpool coaching staff more time to work with captain Steven Gerrard, who was left out of Fabio Capello's squad for Friday's Euro 2012 qualifier in Montenegro as he has played just 56 minutes of football in three substitute appearances this season.
Gerrard's recovery from a groin operation in March took slightly longer than expected but now Clarke believes the 31-year-old can begin stepping up his workload.
"He's coming back from a long-term injury and we'll try to treat him as cautiously and carefully as we can," he added.
"Obviously there will be a time when he is going to have to push on - and I think this is the time now.
"He's going to have to push himself in the coming weeks - and the more minutes we get into him, the better."