Encina reports BriseBois was entering the final season of his current deal. Terms of the contract were not immediately known.
BriseBois' Bolts have won the Stanley Cup the past two years.
The 44-year-old native of Greenfield Park, Que., was promoted to GM from assistant GM in 2018.
BriseBois joined the Lightning as an assistant GM in 2010 after spending nine seasons in the Montreal Canadiens' front office.
BriseBois was GM of the Hamilton Bulldogs, then Montreal's AHL affiliate, when they won the Calder Cup in 2007.