The 36-year-old opted to call time on his career last year, before taking up a role as a Sky Sports pundit alongside Gary Neville and thus finishing without a league winners' medal.
He told the Daily Mail: "It's my one big regret. He was amazing for me and I'd have paid to have him beside me now.
"He and John Terry have been the outstanding centre-halves in this country for years. Talk about having a top mentality. It's just such a shame he wanted to finish.
"Players like him and Stevie Gerrard, the great legends, they become real ambassadors. I'm sure he's no regrets. He's got his job at Sky. I'm sure he'd rather be with Gary [Neville]! They talk football and do great."
Rodgers' current Liverpool squad could take a massive step to securing a first title in 24 years with victory over Chelsea on Sunday afternoon.