Pochettino's brilliant season at St Mary's has made him the clear bookmakers' favourite to take over at White Hart Lane following the dismissal of Tim Sherwood last week.
Rodriguez, who is recovering from a knee injury which ruled him out of the World Cup, said: "It's up in the air and we're not too sure at the moment.
"I'm just trying to focus on my rehab because that's all I really can do, and I don't want to get sidetracked by anything else.
"He (Pochettino) is unbelievable. Anyone will say what a great manager he is and what a good guy he is, to see how well he's done with the type of football we're playing.
"He's worked us hard and we've seen the benefits from it so I think he's a great manager and I love playing under him."
Rodriguez was expected to join Saints team-mates Rickie Lambert, Adam Lallana and Luke Shaw in Roy Hodgson's World Cup squad until he suffered his season-ending injury against Manchester City in April.
The 26-year-old has himself been the subject of speculation about his future - Tottenham are believed to be interested - but is currently more concerned about his rehabilitation. He is not expected to be back in training until October a the earliest.
"There's not really a timescale on when I'll be back," Rodriguez added. "I don't want to rush anything at all because it's important I do everything properly and come back stronger than when I actually finished.
"This is a testing time for my career but I think I'm going to come out of it with a positive ending for me.
"It's going to test me but I think it's going to improve me, mentally and physically."