Clarets boss Vincent Kompany is equipping his side for the challenge of Premier League football after winning promotion from the Championship in impressive style last term.
Tella was a key man in Burnley’s promotion winning campaign and Kompany would like him back.
Relegated Southampton could sell, but want £15m for Tella, a sum which Burnley are not rushing to pay.
Burnley are now prepared to play the waiting game and see if any other clubs come in for Tella and pay his asking price.
The Clarets will hope that Southampton are forced to lower their expectations and accept a smaller fee for Tella later this summer.
At present the 23-year-old is expected to be part of the Southampton squad that reports for pre-season training ahead of the new campaign.
And it remains to be seen if there will be any further developments before the Saints squad assemble.
Burnley kick off life back in the Premier League by playing host to champions Manchester City on 11th August.