Along with the likes of Manchester United and Chelsea, Liverpool are one of the teams touted as a potential destination should Bellingham decide to leave Borussia Dortmund.
Liverpool have already been active in the summer transfer market, bringing in Darwin Nunez from Benfica and Fabio Silva from Fulham but they have also lost Sadio Mane to Bayern Munich.
Barnes believes Jurgen Klopp's side missed a trick by not making a bid for Yves Bissouma, who has since joined Tottenham Hotspurs from Brighton and Hove Albion.
"I think he's a fantastic player," Barnes said of Bellingham. "Another player who I like to have thought would have suited Liverpool, but went to Tottenham, is Yves Bissouma.
"Obviously that's not there anymore because he's gone to Tottenham, but that's the template of the type of midfield player we want.
"A hardworking midfield player, probably more defensive than attacking, who may not score many goals but works hard, wins the ball, gets it forward to the front three quickly.
"Jude Bellingham is similar [to Bissouma]. He probably has a little bit more quality on the ball. He's English, he's young, that would be a fantastic signing for us.
"But it probably isn't going to happen this year. Hopefully next season we could make that signing."
Despite his tender years, Bellingham has been an impressive performer for Dortmund since joining from Birmingham City in the summer of 2020.
The 18-year-old made 44 appearances last season and won the DFB-Pokal the season before.
Bellingham has won 15 caps for the England national team.
