The Brazilian pair linked up superbly in the 6-0 win over Aston Villa.
Firmino joined the club in a big money move from Hoffenheim in the summer and initially struggled, but has started to show his best form in recent weeks.
He has arguably looked his best when compatriot Coutinho is in the team alongside him.
They were inspired in the 4-1 win over Manchester City earlier in the season and once again linked up superbly in the 6-0 win over Aston Villa last time around.
And Coutinho has backed that relationship to improve in the future, hoping it can be beneficial to both club and country.
“Our understanding is improving,” he told liverpoolfc.com.
“I am learning more and more about the way he likes to play, as well as his movement off the ball. Hopefully that can be beneficial to both Liverpool and Brazil.”
“He’s a great player who brings a lot of quality into the squad, but it is not just about two players and a partnership. The whole squad is working to improve as our main objective is to win trophies as a unit.”
Jurgen Klopp will now be hoping he can keep both players, and striker Daniel Sturridge fit until the end of the season at least.
That front three are key to their hopes, with Sturridge in particular looking like the missing part of the jigsaw.
Keeping him fit is the major issue though, with his recent injury list not filling the Reds with hope he can remain fit and firing for the long-term future.