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Hamilton won his third championship with victory at Sunday's US Grand Prix to draw level with racing greats Sir Jackie Stewart and Ayrton Senna.
Mansell believes that fellow Briton Hamilton, 30, is "untouchable".
"Lewis is hot favourite for the 2016 and even the 2017 championship," Mansell told BBC Radio 5 live.
German driver Schumacher's record title haul included five back-to-back titles between 2000 and 2004.
Mansell believes the reliability of the Mercedes car is key to Hamilton emulating Schumacher.
Only once this season, in Singapore, has Hamilton been forced to retire from a race.
Mansell added: "In the present day, no one can touch Lewis. He deserves every accolade. There will be jealousy that he is in the best team.
"It is the start of even bigger and better things to come. I would say [to Hamilton]: Focus on Michael Schumacher's record.
"There is no reason why he cannot win more back-to-back titles. Schumacher has the most reliable car in F1 history, he won three world championships on reliability alone."
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Nico Rosberg was less than gushing in his post-race interview towards his Mercedes team-mate - even throwing a cap at him.
But other sporting champions were quick to pay more fulsome tributes, beginning with F1 drivers past and present...
Lewis Hamilton should target Michael Schumacher's record of seven world titles, according to 1992 champion Nigel Mansell.