Ralph Hasenhuttl appears to be having an immediate impact on his side, having overseen three wins and a draw in his last six Premier League games.
Nevertheless, he is apparently keen to improve his options this month. The Sun on Sunday (13/1; page 59) reports that the Saints have joined Leicester City and Bournemouth in the race to sign Mepham, who is rated at £15 million.
The Wales international has made 22 Championship appearances for the Bees this term, and is establishing himself as one of the finest centre-backs in the second tier.
The report adds that the Saints may be willing to move a player on to ensure that they have the funds to make a deal happen, which perhaps provides an indication of how highly Hasenhuttl and his team rate the 21-year-old.
Southampton look a much more difficult side to break down since Hasenhuttl arrived. But they have still only managed to keep one clean sheet during his tenure, so strengthening their options at the back must be a key priority during this window.