It is claimed that the pair are 'expected' to sign for Liverpool and Manchester United respectively, over the next two transfer windows, and the Saints, it seems, have a contingency plan in place.
Wimmer signed a new five-year deal at White Hart Lane only this summer, but has fallen out of favour with Tottenham head coach Mauricio Pochettino, whose defensive options already include Toby Alderweireld, Jan Vertonghen and Eric Dier, along with promising teen Cameron Carter-Vickers.
Southampton, though, could face competition for Wimmer, who the report claims is rated at £6 million, with Bundesliga side Borussia Monchengladbach said to be keen.
The Austrian spent three seasons in Germany with FC Cologne, before moving to north London in summer 2015.
Tottenham have taken Gareth Bale, Victor Wanyama and Pochettino from the Saints this past decade, while Alderweireld spent a season on loan to St. Mary's from Atletico Madrid. In contrast, Wimmer would be the first Spurs player to move to the south coast club since Tommy Forecast in 2008.