A ruptured cruciate ligament has kept the 25-year-old striker on the sidelines for more than a year but several of Saints' top-flight rivals had been linked with a move for Rodriguez, whose current contract only had a year to run.
But Southampton have kept him at St Mary's and manager Ronald Koeman told saintsfc.Co.Uk: "It's very good news for the club because there was some speculation about Jay and interest from other big clubs.
"He has signed until 2019, which is great news because it is a good signal to everyone inside and outside the club that he believes in the future of Southampton.
"We had hopes that he would be back for January because he is a good forward player who gives us great options.
"But he is close to being back now and after an Under-21 game he might be in the squad for the Manchester City game," Koeman said.
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