Tella impressed while on loan at Burnley last season and helped the Clarets to win promotion to the Premier League.
Burnley have been seeking to sign Tella on a permanent basis, but have been unable to agree a deal with Southampton for his signature.
Now Leverkusen are working to take Tella to Germany and, according to German magazine Kicker, there are growing signs that he will soon be heading to the BayArena.
It is suggested that Leverkusen will splash out €20m to sign the speedy winger.
Leverkusen lost winger Moussa Diaby to Aston Villa earlier this summer and Tella could slot in as a replacement.
Tella has already turned out for Southampton this season, playing in Saints’ opening three Championship fixtures.
The winger netted in Saints’ win over Plymouth Argyle in the Championship last weekend.
