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Sources confirmed to CBSSports.com that the two sides have talked about Smith, who was fired last week by the Gophers, taking over in Lubbock. Chris Walker was the interim coach this past season after Billy Gillispie was fired just before the start of the year.
ESPN.com's Jason King first reported that Smith and Texas Tech were in discussions about the vacancy.
Smith spent the past six seasons at Minnesota and won just a single NCAA tournament game, earlier this month against UCLA.
The Red Raiders have also been in contact with former Nebraska coach Doc Sadler, Southern Illinois coach Barry Hinson, Oral Roberts coach Scott Sutton and Indiana assistant coach Steve McClain -- among others.