Everton’s Tom Davies is the most recent player in that position to be linked to a Saints move.
However, a previously-linked target, Leicester City’s Hamza Choudhury, is reportedly looking for a move away from the Foxes.
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Earlier in September, the Telegraph’s Mike McGrath linked Southampton with Choudhury.
Now, talkSPORT is reporting that the 22-year-old wants a permanent move away from the King Power Stadium after falling down the pecking order under Leicester manager Brendan Rodgers.
Currently, Nampalys Mendy is preferred by Leicester over Choudhury.
Choudhury, who has seven England caps at Under-21 level, made 20 appearances for Leicester in the Premier League last season, scoring once.
When does the summer transfer window open and close?
The summer transfer window opened on 27 July and closes at 23:00 on 5 October.
A domestic-only window for trades between Premier League and EFL clubs will run from 5 October until 16 October at 17:00.