The Parkhead striker still considers the former England captain "world class" and is hopeful he will snub a return to Liverpool in favour of the Scottish champions
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The former England captain has options to continue his illustrious playing career as well as move into coaching after deciding not to renew his contract with LA Galaxy and leave MLS.
His former Liverpool manager Brendan Rodgers is reportedly front of the queue with regards to offering Gerrard a playing contract, although the former Anfield skipper has been linked with returning to his boyhood club as a coach.
Current Anfield boss Jurgen Klopp had said Gerrard would "always be welcome" at the club, but Sinclair is hopeful he will see the 36-year-old don the famous kit of Celtic next.
"It'd be a massive thing if he did come here, that would be unbelievable," Sinclair told a press conference. "I think the fans would take to him and it'd be a massive deal in football.
"He's a world-class player so I'm sure that a lot of players would learn from him."