Tottenham are instead now being linked with moves for Saido Berahino and Jackson Martinez - but it is understood Mauricio Pochettino would also hold an interest in bringing his former striker to White Hart Lane.
Pochettino, of course, worked with Rodriguez when he was Southampton boss.
But the 25-year-old, say the People, only has eyes on staying at St Mary's. And the news that he could return from a lengthy knee injury in January will surely please Southampton fans.
Graziano Pelle has been superb for the Saints since joining the club in the summer but has suffered a dry spell in front of goal in recent weeks.
Rodriguez's determination to earn a new deal, then, is good news for Southampton - but bad news for Tottenham.