Firmino comes off contract in June.
"Firmino is my favourite striker in terms of what he gives his team not just in terms of scoring goals but work rate," said Barnes, speaking to BonusCodeBets. "He's the reason (Mohamed) Salah and (Sadio) Mane scored all of those goals because of the way he plays. If Bobby left, I would be very sad
"Obviously we have (Darwin) Nunez who plays differently but I would always keep Bobby. And if he left, I would be very sad."
Barnes added: "He has to decide if he wants to play regularly but if it was up to me I would definitely keep Bobby."