Reports in the British media suggested that manager Jurgen Klopp identified Bowen as a key target this summer.
Bowen has been with the Hammers for 18 months, signing from Hull City.
He managed eight goals and five assists in the Premier League last term.
"Personally I don't think he [Bowen] is the type of player that Liverpool need," former Reds defender Johnson told BettingOdds.com.
"He's a good player, he's proved a lot of people wrong and he's stepped up in the Premier League but I don't think he's at Liverpool's level.
"I think Liverpool have better players already so I'd be surprised to see them offload anyone to bring in Bowen.
"He's had a good season and his career is going in the right direction and if he keeps improving then you never know what will happen. Right now though I don't think he's a good fit for Liverpool."
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