Southampton are looking to bolster their defence after the January departure of Virgil van Dijk to Liverpool.
Southampton narrowly survived relegation this season, but they need to make sure they bolster the squad properly in order to avoid a similar struggle next season.
The report claims that the Saints are pressing ahead with their transfer targets, and signing a left-footed centre-half is a top priority.
The 25-year-old made his senior debut for Boro in 2010 after graduating from the club academy and has made over 200 appearances for the club.
With Boro failing to secure promotion to the Premier League after they lost to Aston Villa, it remains to be seen how long they can hold on to him, especially with so many Premier League clubs vying for his signature.
Gibson is reportedly on £20k-per-week wages, and meeting his salary won’t be a huge problem for the Saints.