Lynch took over as Larne manager in 2017 and led them from the second-tier Championship to back-to-back top flight titles.
He also guided them into the Uefa Conference League phase this season as Larne became the first Northern Irish side to qualify for the group or league phase of a major European competition.
The 44-year-old previously rejected the chance to take at Scottish Premiership club St Johnstone in September.
Larne are sitting ninth in the Irish Premiership table after a stuttering start to their title defence.
The Inver outfit are 14 points behind pacesetters Linfield with three games in hand after a 1-0 home defeat against the Blues at the weekend.
Lynch would be tasked with overseeing a rebuild at Derry following a disappointing fourth place finish in the Premier Division last season.
The Candystripes were locked in a title race with eventual champions Shelbourne for much of the season but that league finish – coupled with the cup final defeat – means Derry will not play European football next season.
They have also lost brothers Shane and captain Patrick McEleney to Glentoran and Ballymena United respectively as well as Colm Whelan to Bohemians following the expiration of their contracts.
