Despite Saints manager Nigel Adkins denying a move for the 24-year-old following their defeat to Wigan last weekend, a deal is expected to be reached before the close of the transfer window.
The newly-promoted side have been chasing defenders following their promotion to the Premier League to increase competition at the centre-back positions currently occupied by Jose Fonte and Jos Hooiveld.
Yoshida has made 17 appearances for the Japanese national side and captained his country at the Olympics in London where they finished in fourth place. In two years at Venlo the 24-year-old has played over 50 games, scoring five goals.
If the Saints are to reach an agreement with the defender he will become their sixth signing of the summer, following Steven Davis, Nathaniel Clyne, Paulo Gazzaniga, Jay Rodriguez and Emmanuel Mayuka to arrive at St Mary’s.