Spurs manager Mauricio Pochettino is again believed to be lining up a move for his former player having failed to secure the English striker in the summer transfer window.
Andros Townsend, who was close to leaving White Hart Lane in the summer, could again be used as a makeweight for Rodriguez, though West Ham are also said to be watching the England winger.
Southampton bosses refused to sell the £15m-rated Rodriguez or Morgan Schneiderlin to their former manager in the summer, after Adam Lallana, Luke Shaw, Calum Chambers and Rickie Lambert all left St Mary's.
The south coast club have not missed the 25-year-old, who has not played since injuring his cruciate ligament against Manchester City in April, with Graziano Pelle firing Ronald Koeman's team to second in the table.
With Southampton impressing without Rodriguez, the top English scorer in the Premier League last season, and his contract having just 18 months left to run in January, the Daily Telegraph report that Pochettino will again make a move.
One player now reported to not be heading to Spurs is former Chelsea, Portsmouth and Arsenal midfielder Lassana Diarra.
The Frenchman, currently a free agent, had been linked with a potential move to White Hart Lane but the Daily Mail report the club are unable to sign any free agents as their Premier League squad is set.Reuse content