Southampton are expected to make a number of additions over the coming months.
The Saints are plotting to increase the depth of their squad in the summer and are said to feel that Djilobodji could be a good option for the side.
The central-defender has been a mainstay for Nantes this season and his performances have won him a number of plaudits.
Nantes are keen to keep hold of the 27-year-old, but he has just one year left on his contract and they realise that they cannot afford to lose him on a free.
As a result, a bid of £5 million would reportedly be enough to convince the Ligue 1 to sell up, and it is thought that Southampton could be prepared to meet that asking price.
Ronald Koeman wants to add more quality to his defence this summer and Djilobodji could come in as a replacement for Toby Alderweireld.
Alderweireld has impressed at St. Mary's while on loan from Atletico Madrid, but Southampton are apparently starting to become concerned that they may not be able to make his stay a more long-term one.
As a result, they are making a contingency plan and feel that signing Djilobodji would soften the blow of losing the Belgian international.