"It appears that Kevin now wants and intends to become a free agent in order for him to try and find a new club either in this country or in Australia."
Salford owner Marwan Koukash confirmed the club had received the letter but said he would not respond publicly until he addressed a media conference on Tuesday at the AJ Bell Stadium.
"He has sent a resignation request to the club," Koukash confirmed to Press Association Sport.
"We have not yet responded.
"I will be making a full statement, revealing our side of the story, on Tuesday."
Locke, who played for the Kiwis in the 2013 World Cup final at Old Trafford, was viewed as a marquee signing by Salford when he joined almost a year ago on a three-and-a-half-year deal after leaving the Warriors and NRL.
But Locke endured a turbulent time at the club, playing in just 13 out of a possible 27 matches since making his debut last July at Huddersfield.
Injuries played a factor but Koukash made his feelings clear in recent weeks when he said he was prepared to listen to offers from rival clubs to buy Locke mid-season.
Locke even considered a switch of codes earlier this year when he held talks with the Scottish Rugby Union before the idea was abandoned when chief executive Mark Dodson withdrew from negotiations.
Reports out of Australia last week suggested he was recently shopped around various NRL clubs with the Canberra Raiders said to be keen on securing his services for 2016.
