Antenucci, 31, was the club's second top-scorer last season, scoring nine times as Leeds finished in 13th.
He moved to Elland Road from Serie A side Ternana in 2014 and scored 19 goals in total for the Whites.
Leeds have offered a new deal to 17-year-old goalkeeper Bailey Peacock-Farrell, who made his debut against Queens Park Rangers in April.
BBC Radio Leeds also understands that all parties charged by the FA over the transfer deal involving striker Ross McCormack's from Leeds to Fulham in 2014 have been given an extra week until close of play May 27 to respond.
Leeds United and licensed agent Derek Day have been accused of breaching The FA's Football Agent Regulations whilst United chairman Massimo Cellino faces a charge of breaching FA Rules."
BBC Radio Leeds also understands that the club and owner Massimo Cellino have been given an extra week to respond to charges by the Football Association that they breached football agent regulations over the transfer of Ross McCormack to Fulham in July 2014.