Neither player has amassed much game time for the Reds so far this season - indeed, Enrique has played four minutes in the league, while Suso is yet to appear - but this weekend's trip to Upton Park could provide a change.
For Enrique, of course, the difficulty now lies in displacing Alberto Moreno, the £12 million summer signing who has made a terrific start to life at Anfield.
But, for Suso, there may just be an opportunity to influence proceedings as boss Brendan Rodgers looks to vary things up in Liverpool's midfield.
The Spanish duo have become good friends on Merseyside and are often seen together on social media - and both could have a big part to play this season.
Suso's chances of participating at Upton Park may be affected by two factors, however. Firstly, the Reds' current lethargy going forward might see Rodgers seek different options in midfield.
And, secondly, the 20-year-old has been heavily linked with a January move to AC Milan next season.
How better to convince Suso he has a role to play at Anfield, then, than by actually giving him a role to play at Anfield?