After failing to reach terms with Chelsea for the France No1 before last Tuesday's Club World Cup transfer deadline, they're expected to try again after the tournament.
As it stands, Milan will be forced to sell with Maignan having just over a year to run on his contract.
Makelele told BBC Sport: "Maignan is currently one of the best goalkeepers in the world. I imagine Milan do not want to lose their goalkeeper, but if Chelsea could bring him to London it would be a huge reinforcement, because to win trophies you need a reliable goalkeeper.
"Look at PSG: they had a young team, but an exceptional goalkeeper in Gianluigi Donnarumma. Chelsea need a goalkeeper, a striker and possibly a winger to be able to seriously compete in both the Champions League and the Premier League next season."