The Saints have been majorly active in the closing week of the transfer window, closing or nearly coming close to a number of deals.
Wolfsburg star Lacroix is another name on their radar in the closing stages of the window, with the defender an option to strengthen the backline.
Lacroix played 29 times for the German club last term in the Bundesliga and his displays caught the eye of Southampton.
Despite their interest in the centre-back though, Southampton are now unlikely to bring Lacroix to St. Mary’s.
With the window nearing conclusion, it is thought it will be too late for Southampton to have time to reach a deal for the centre-back.
Southampton are on the verge of losing centre-back Jan Bednarek, but have Duje Caleta-Car lined up as replacement.
The Saints are also looking to improve in other positions and have deals lined up for multiple players on deadline day.