The Foxes captain has been told he can leave the club, relegated to the first division last season, due to financial reasons.
Elliott moved to Glanford Park from Torquay United in 1992, featuring in the fourth division playoff final defeat at the hands of Blackpool, before moving onto Oxford United for £150K in the November of 1993.
His £1.6million switch to Filbert Street in 1997 earned the Iron a £300K windfall in a sell on clause, and he helped the side to two League Cup victories and represented Scotland.
"I've told Matty it's a financial decision rather than a football decision, "explained Leicester manager Micky Adams, "he is fully aware of that but we have to cut our cloth accordingly."