The Charlton Athletic star is out of contract in the summer and can be acquired for a nominal cross-border compensation fee.
Lennon has kept tabs on the player since replacing Brendan Rodgers as caretaker manager back in February.
With him set to be confirmed as his countryman's successor on a permanent basis, he's looking to bring in Aribo as he starts to shape his squad ahead of next season.
The 22-year-old has racked up nearly 100 league appearances for the Addicks and was previously linked with Rangers.
Charlton haven't yet given up hope of convincing the player to stay with the club after they won promotion to the Championship.