The Glasgow giants granted Leicester permission to speak to Rodgers on Tuesday morning and the Northern Irishman is believed to have already travelled south.
The Premier League club, who currently sit 12th in the table, eight points above the relegation zone, want the former Liverpool boss to take charge at the King Power Stadium after Claude Puel was sacked on Sunday.
Rodgers has won every domestic trophy on offer in Scotland during his two-and-a-half years in charge at Parkhead - seven in all - with the club currently on course to win the treble for the third season in a row.
It had been widely expected that Rodgers would see the season out before heading back to England, with Lennon even mentioned as a possible interim manager at Leicester.
However, it now seems Lennon will return to the Celtic hotseat almost five years after initially leaving it.
The former Celtic and Leicester midfielder departed Hibernian by mutual consent last month.
He could be in charge for Wednesday's Premiership game at Hearts, according to reports in Scotland.
Rodgers, meanwhile, looks likely to take the Leicester reins for the first time at Watford on Sunday.
Leicester face Brighton at home on Tuesday night, with Mike Stowell set to take charge.
Rodgers, 46, is expected to take his backroom staff with him to the King Power.
He managed Liverpool for just over three years, famously leading them to the brink of the Premier League title in 2014 before a late slump saw them pipped by Manchester City.