While the Merseysiders are expected to use much of the £142m (€160m) fee they could eventually earn from the sale of Coutinho on new players, they are also prepared to invest in their current squad.
And Firmino is next in line to be rewarded for his significant improvement.
The Brazil international has just under two-and-a-half years to run on his current Liverpool deal, but the club are planning to offer a contract that will keep him at Anfield for the rest of his career, according to The Daily Telegraph.
Though Liverpool are not said to be concerned that any of their remaining key assets want to follow Coutinho out of the exit door – Sadio Mane and summer arrival Mohamed Salah are believed to be settled – they want to ward off any potential bids from rivals in Europe.
Talks between Firmino and Liverpool have not yet begun, but they are imminent and could lead to the 26-year-old remaining at the club for at least another decade.
Since arriving as a relative unknown quantity in the summer of 2015, Firmino has scored 39 goals and made 30 assists in 120 appearances for Liverpool.
Yet it his pressing game and synergy with Mane, Salah and Coutinho, before his exit, which has defined his success with the Reds and seen him leapfrog Daniel Sturridge in the pecking order.
Such is manager Jurgen Klopp's delight at Firmino's work without possession, he recently described the former Hoffenheim striker as an "annoying" player for opposing teams to play against.
News that Firmino's contract could be extended follows the player's heartfelt message to international compatriot Coutinho, in which he said that life at Liverpool would never be the same again without the playmaker.
"Liverpool is no longer the same without you my magical brother," said Firmino on Instragram. "I wish you infinite success, that you enjoy life and realise all your dreams brother. God is always protecting you and your whole family. It was an honour to play with a magician like you."