Rafael Benitez is expected to depart the Blues at the end of the season, with Moyes just one of a number of names linked with the role at Stamford Bridge.
However, Sinclair told talkSPORT: "Everyone knows what he's done at Everton is superb but, to be honest, I don't know if Chelsea is the right job for him.
"He's used to keeping a club like Everton afloat on not a lot of money, but they haven't won anything in a long time.
"Being Chelsea manager is about winning things. If you don't win things then, as far as the supporters are concerned, it's a poor season."
Sinclair represented Chelsea for eight years from 1990 to 2008.