The proposed extension was presented before the tournament, with Pochettino’s current deal set to expire at its conclusion.
The Argentine has previously expressed his desire to remain in charge for a second cycle, provided the conditions are right.
He has also revealed that he turned down approaches from other clubs because of his commitment to the USMNT.
U.S. Soccer CEO JT Batson confirmed that discussions over a new contract have been ongoing, raising hopes that Pochettino will continue leading the national team after the World Cup.
"We've had a number of very long discussions around what the next four years could look like," he said.
"We're excited, and they're excited, but, of course, we've got to focus on the summer and we're doing that."
The United States will face Bosnia and Herzegovina in the round of 32 of the ongoing World Cup.