With Mikael Lustig and Cristian Gamboa having departed on free contracts and Jeremy Toljan returned to parent-club Borussia Dortmund after his loan spell it has the Scottish champions understaffed in the position.
Anthony Ralston is the sole out-and-out right-back option, yet Lennon has opted to play Kristoffer Ajer in the role for the club's Champions League first-round qualifying matches against FK Sarajevo.
Former Leicester City star Danny Simpson could be the player to fill the position.
The 32-year-old is set to join Celtic on trial following his release from Leicester City, according to the Scottish Sun.
During five years at the Foxes the former Manchester United youngster made more than 130 appearances for the club, helping the club win the Premier League in 2016.
Parkhead boss Lennon has admitted that there will likely be movement in the transfer market in the coming days with right-back earmarked as a "priority".
“I think we’ll have something in the next few days hopefully," he said. "It might be a right-back, it might be a left-winger, it might be a centre-forward.
“Right-back is a priority, but we have a number of positions I’d like to strengthen like midfield and one or two attacking areas.
“You don’t want to overcook it either, but we want to add to the quality in the squad that we already have.
“The boys are doing a brilliant job at the minute, but they could do with a little bit of help in terms of strength in depth.”