He was formerly dual assistant manager of Middlesbrough and the Republic of Ireland, but left both roles in 2020.
The 42-year-old is now set to return to coaching with struggling Leeds, who are poised to sack Javi Gracia and appoint Allardyce as boss.
Former striker Keane put pen to paper with the Elland Road club on Tuesday morning, according to The Times.
Keane previously spent time at Leeds as a player, initially on loan from Inter Milan, before joining permanently in May 2001.
And he will reportedly return to the club over 20 years later as part of Allardyce’s coaching staff.
The Times also say former England boss Allardyce will land £3MILLION if he keeps Leeds in the Premier League.
He will earn a basic salary of £500,000 and a bonus of more than £2.5m if he keeps Leeds up.
But he will be without trusted assistant Sammy Lee, who is currently on jury service.
So ex-MK Dons and Oxford United manager Karl Robinson is set to be Allardyce’s No2 instead.
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And Keane will also reportedly be part of Allardyce’s staff.
As well as his time as assistant manager of Middlesbrough and the Republic of Ireland, Keane spent three games as player-manager of Indian side ATK back in 2018.
Keane played 56 games in total for Leeds, scoring 18 goals, before leaving to join Tottenham in 2002.