Tanner said 19-year-old Luke Thomas, who started the 3-0 win over West Bromwich Albion on Thursday, could benefit from a season out on loan where he would play week in, week out.
Elsewhere, 22-year-old James Justin could be out until November after rupturing his anterior cruciate ligament in February.
And Christian Fuchs, part of the Foxes’ title-winning squad, could leave as a free agent this summer as he reaches the end of his contract.
Bertrand ‘would go against Leicester philosophy’ but solve problem
Tanner reckons that, because Leicester have two youthful options who will compete for the left-back position in years to come, it would make sense to target a short-term solution.
“One of the possible targets that would fit that bill is somebody he’s worked with Chelsea and who’s out of contract at Southampton – Ryan Bertrand,” he said.
“Whether he will go for a player that’s 31, that would go against the club’s recruitment philosophy.
“In the short term, holding down the fort for Thomas to develop and Justin to get back to his best, that might be a solution.”
This season, he’s been averaging 2.1 tackles, 1.3 clearances and 0.5 key passes per 90 minutes for the Saints (via WhoScored).
The Englishman is valued at £9million by Transfermarkt.
Leicester, Tanner added, are expected to target up to five reinforcements if they qualify for next season’s Champions League.