England international forward Rodriguez has featured in all 31 of the Saints' Premier League matches so far this season and is also their top scorer on 15 goals.
However, Rodriguez could miss the game against the Magpies at St Mary's on Saturday after he was forced out of last Sunday's 3-2 defeat at Tottenham with a knee problem.
Schneiderlin and Wanyama both missed the game at White Hart Lane with respective hip and leg problems and are again struggling to be fit, while Steven Davis has suffered a slight groin injury which will need checking.
Kelvin Davis, Nathaniel Clyne and Maya Yoshida are also definitely out with respective hip, groin and knee ligament problems.
Boss Mauricio Pochettino bemoaned the "long list" of injuries he has to contend with while he revealed that Yoshida's injury is the biggest cause for concern. But he is hopeful the player will be available for Japan's World Cup campaign in the summer.
He told the Daily Echo: "It is true he will be out for six or seven weeks but his participation in the World Cup will not be threatened.
"It will be difficult for him to play in the last six weeks of this season."