Smith, who played from 1987 to 1997 with six NBA teams, has never coached in the NBA.
ESPN's Adrian Wojnarowski reported earlier this week that the four top candidates are former Memphis Grizzlies coach David Fizdale, former Golden State Warriors coach Mark Jackson, former Cleveland Cavaliers coach David Blatt and former Toronto Raptors assistant Jerry Stackhouse.
The expectation was that three of the four would interview this week, with Blatt's interview coming next week.
New York also received permission to talk to former head coach Mike Woodson, who now is serving as an assistant for the LA Clippers, sources told ESPN. Woodson, who was fired by the Knicks in 2014 after two-plus seasons at the helm, isn't considered to be in the top tier of initial candidates.
Knicks president Steve Mills -- a former teammate of Blatt's at Princeton -- and general manager Scott Perry are conducting the search, which was to include interviews with candidates beyond Fizdale, Jackson, Stackhouse, Blatt and Woodson, league sources said.
The Knicks fired coach Jeff Hornacek last week after seasons of 31-51 and 29-53 in New York.