The Brazil international struggled for form in the immediate aftermath of his £29 million move to Anfield from Hoffenheim, but has thrived under Jurgen Klopp and has had a direct hand in 11 Premier League goals in 2016.
And after the 24-year-old found the net in Thursday's Europa League win over United, Scholes hailed the forward for his recent form.
"You saw the gulf in quality here, it was just incredible," he told the Daily Mail. "Look at the forward players Liverpool had: [Philippe] Coutinho, Firmino, [Daniel] Sturridge. They've got goals.
"I hadn't been sure about Firmino but this last week he has convinced me. He's been brilliant."
Scholes also admitted he has been impressed by Adam Lallana's performances in recent weeks, and has not ruled out Klopp leading the Reds to the Champions League this season.
READ MORE | Klopp: We could have scored more
"Lallana had a quiet period but he looks like a real player. Before the Liverpool versus Manchester City game, which I worked at, I was thinking, 'Klopp might only keep two or three of these'.
"But what is he building now? They need to go on from here. They can go on from here.
"They could even finish in the top four in the Premier League this year if it carries on."