Following his dismissal by Shamrock Rovers last season, the former Derry City manager is in line to take over at Oriel Park
The Dubliner was sacked by the Hoops midway through last season after a disappointing run of results saw them fall adrift in the league and also exit Europe.
According to a report in the Irish Independent, the former Dunfermline boss has held extensive talks with the Co Louth club over becoming their new manager.
Despite leading the club to Premier League survival, the Lilywhites board opted against retaining the services of previous manager Darius Kierans but hopes of appointing Kenny as his replacement immediately were delayed because of an on-going dispute with Rovers over his severance package.
Despite his brief spell at Tallaght, Kenny has enjoyed over a decade of success in management both in the League of Ireland and Scotland.
He became the youngest manager in league history when he took over Longford Town at the age of 27 in 1998. Kenny enjoyed huge success during his three year tenure in the Midlands before having spells as Bohemians, Derry City and Dunfermline manager.
He has also been linked with the vacant post at Limerick after the Shannonsiders sacked Pat Scully last week but it seems Dundalk have won the race secure his signature.
An announcement from Dundalk on their new manager will be made at 14:00 GMT on Thursday.