The Blaugrana's pursuit of Coutinho throughout the summer was well-known, though the Premier League side eventually held firm despite offers for their star man.
Barca chief executive Oscar Grau recently suggested the club were ready to make another move for the playmaker in midseason, per Sam Marsden of ESPN FC.
When asked about a January move for Coutinho, Valverde revealed he wanted any incoming business to be done without fuss.
"If there is interest in signing any player in January who's not here at the moment, I wouldn't like it to be broadcast all over the world," the coach said, per Marsden. "I'm more interested in [B-team players Carles] Alena, [Jose] Arnaiz and [Oriol] Busquets than other players at other teams."
As relayed by Marsden, speculation about a possible move in the upcoming transfer window has gathered pace again, as Barcelona technical secretary Robert Fernandez was reportedly at Wembley Stadium on Sunday to watch Coutinho's Liverpool lose 4-1 to Tottenham Hotspur.
As noted by Kevin Mitchell of the Guardian, while the Reds were dominated by Spurs, there were some moments to remember from their No. 10:
kevin mitchell @kevinmitchell50
Got to say, Coutinho is sublimely skillful, regardless of the situation. A lost soul here, though.2017-10-22 16:32:27
Coutinho was keen to make the move to Barcelona in the summer.
While he would have been disappointed it didn't go through in the end, in the main he's been brilliant since being brought back into the side by Reds manager Jurgen Klopp.
Whether on the left flank or in midfield, his linkup play, delicate manipulation of the ball and ability to strike from distance has given Liverpool a different edge in the final third.
It's why Barcelona may not have given up on the 25-year-old yet. The way in which Coutinho plays aligns well with the Blaugrana traditions.
World Soccer Talk's Kartik Krishnaiyer is unsure whether the Liverpool man should be considered in the elite bracket:
Kartik Krishnaiyer @kkfla737
Coutinho is such a frustrating player. Produces such moments of magic but for me has never been consistent enough to be a top player.2017-10-22 15:42:07
While there are undoubted inconsistencies to Coutinho's game, he has improved under Klopp. And you sense alongside better players at the Camp Nou that standard would only be enhanced further.
The pursuit of the player became something of a circus during the summer, and it's understandable that a straightforward coach such as Valverde would prefer to do without that. You would imagine some lessons have been taken on board.
Even so, the prospect of Liverpool selling such an important player halfway through the campaign seems unlikely.