Joint hosts USMNT were knocked out of the tournament at the hands of Belgium, who swept them aside with a comfortable 4-1 win.
Their campaign was marred by controversy after FIFA decided to suspend Folarin Balogun’s red card at the behest of President Donald Trump.
Following the USMNT's World Cup exit, Pochettino, 54, was asked about his future and he refused to be drawn in.
“In the next weeks, we can start to talk if the federation wants to talk,” Pochettino said.
“Right now, it’s about resting a little bit, to think, have conversations with the federation to see what the decision is. I’m so happy. We’ve built a very good relationship. Now is not a moment to talk.”
On Tuesday, U.S. Soccer put out its own statement, saying: "We had positive conversations with Mauricio before the World Cup about the future.
"We agreed we would continue those conversations following a chance to rest and reflect post-World Cup. We have a great deal of respect and gratitude for Mauricio, his staff and everyone part of the program.
"We have shared excitement about our potential and also shared clarity about the amount of work at all levels still required to achieve our ambition."