The Dutchman lodged an official transfer request this week and released a lengthy statement on Monday confirming his desire to move on from St Mary's Stadium, while also denying suggestions that he has refused to train.
Although the Saints are reportedly continuing to play hardball over Van Dijk, The Sun claims that they are nonetheless making contingency plans to replace the talented defender.
The report suggests that Gibson, one of Boro's shining lights in the Premier League last season, is deemed a suitable replacement for the Netherlands international.
However, it is also believed that the Teessiders do not want to sell the 24-year-old, but could be persuaded into doing a deal if a bid of at least £30m comes in.
West Bromwich Albion, Chelsea and Tottenham Hotspur have also been credited with an interest in Gibson, while Liverpool are believed to be frontrunners for Van Dijk's services.