The Foxes have endured a well-documented period of frustration in the transfer market, a consequence of FFP restrictions and squad-number limitations.
That has been partially eased with a couple of outgoings, but backup goalkeeper Alex Smithies remains the only additions during the summer window.
However, with Wesley Fofana and Youri Tielemans continuing to be linked with a big-money transfer elsewhere, Brendan Rodgers could be provided with the chance to finally bring in at least one fresh face.
According to The Times, Rodgers hold an interest in securing the services of Pepe over the coming week.
The Ivory Coast international has failed to play a single minute of Arsenal's opening three Premier League fixtures, all of which have ended in victories.
When quizzed on the matter before the latest triumph over Bournemouth, head coach Mikel Arteta hinted that permission had been given for Pepe to find a new team.
The Spaniard told reporters: "What we can communicate we always do when it's the right moment. We discussed that we have a big squad and we've made some decisions and allowed some players to leave.
Reports have suggested that Pepe would prefer a return to Ligue 1, where he previously excelled for Lille and earned himself a £72m transfer to the Emirates Stadium.
Transfer expert Fabrizio Romano has previously indicated that the two parties are in discussions over a loan agreement for the attacker.
As it stands, that appears to be the most likely conclusion for a player is eager to secure regular first-team football during 2022-23.
During the last campaign, Pepe was provided with just 681 minutes of Premier League football, contributing only one goal and two assists.
In total, the wideman has provided 16 goals and nine assists from his 80 outings in England's top flight, although Rodgers may be prepared to hand Pepe the game time that he craves in the East Midlands.
Leicester have only recorded one point from three games with James Maddison the only attack-minded player to make an impression this campaign.