Tella has been on the books of the Saints since joining their youth set-up in 2017 from Arsenal’s academy.
After failing to establish himself at St Mary’s as a regular starter, he was sent on loan to Burnley last season, where he scored 17 goals in 39 Championship games, helping them secure promotion to the Premier League.
Burnley want Tella back on a permanent basis, but have been unable to agree a deal and now Leverkusen are are pressing ahead with their efforts to sign him.
According to Sky Deutschland, the German outfit are keen on landing Tella and they have a verbal agreement with the player.
However, Leverkusen and Southampton have yet to agree on a fee for Tella.
Moussa Diaby has joined Aston Villa from the Bundesliga club and they are eager to fill his void with the 24-year-old winger.
Tella still has two years remaining on his contract with the Saints, which puts the Championship outfit in a good position to demand a high transfer fee.