The 25-year-old ruptured an anterior cruciate ligament at the back end of last season against Manchester City which forced him out of the World Cup.
Mauricio Pochettino is reportedly expected to be handed a £20m transfer kitty in January, with Rodriguez and his team-mate Morgan Schneiderlin touted as possible targets.
But Saints boss Ronald Koeman may deter Spurs from pressing ahead with a bid after providing an update on Rodriguez's injury.
GETTY
Jay Rodriguez is set to be out for another six weeks
He needs time and we are giving him the time to come back, but it's a pity because he's a great player
Ronald Koeman
"After a big injury, you don't have to rush. He needs time and we are giving him the time to come back, but it's a pity because he's a great player," Koeman said.
"I think now, in this situation, he will not be available before the end of January."
It remains to be seen whether Pochettino will back off from Rodriguez.
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