The Premier League strugglers are looking to back Nathan Jones in the transfer market this month and they have already snapped up Croatia international Mislav Orsic.
Racing Club midfielder Alcaraz is wanted at St Mary’s, but there is significant competition for his signature, not least from Portuguese giants Benfica.
However, Southampton are remaining in the race and are trying to secure him.
Alcaraz is considered to be a bright prospect for the future and fits within Southampton’s policy of snapping up young talents.
He is expected to cost above the £12m mark for whoever secures his signature this month.
Southampton sit rock bottom of the Premier League table and have only won three of their 18 games so far; it is unclear if their plight will affect Alcaraz’s decision.
Jones’ side next face Manchester City in the EFL Cup on Wednesday before then travelling to take on fellow strugglers Everton in a crunch league clash.
