Vettel told Sky Sports television on Wednesday that he was "potentially" in the market for a 2025 comeback and was talking to Mercedes boss Toto Wolff and others.
"I would love for Seb to come back and I think he would be an amazing option for the team," Hamilton, who joins Ferrari next season, told a press conference at the Suzuka Circuit ahead of the Japanese Grand Prix.
He said the German driver would be good fit for the German manufacturer and that Vettel's racing pedigree and values would push forward a team trying to revive the form that delivered seven back-to-back drivers championships between 2014 and 2020.
Mercedes last had a German driver with Nico Rosberg, who retired after winning the 2016 world championship
Seven-time world champion Hamilton has previously described Vettel as his favourite Formula One rival over the years. Vettel finished runner-up to Hamilton in 2017 and 2018 before calling time on his career at the end of 2022.
Vettel recently tested a Porsche Penske Le Mans hypercar and could debut in that 24-hour race.
Hamilton's Mercedes teammate George Russell also said it would be good to see Vettel back on the track.
"Sebastian's a great person ... For sure his personality is missed on the grid and I think it's important that we have the best 20 drivers in the world all competing for race wins and championships," he said.
"I'm really happy and open to have anybody as my teammate, whether it's a world champion or a rookie it doesn't change how I go about my business."
