Story highlights Trump was invited to the summit by Indian Prime Minister Narendra Modi in June

A Senior State Department official told CNN: "They (Tillerson and his staff) won't send someone senior because they don't want to bolster Ivanka"

(CNN) Days ahead of what should be a major moment for Ivanka Trump on the world stage, CNN has learned Secretary of State Rex Tillerson isn't sending a high-level delegation to support her amid reports of tensions between Tillerson and the White House.

Multiple State Department officials, as well as a source close to the White House, have told CNN Tillerson's decision not to send senior State Department officials to this year's Global Entrepreneurship Summit, being held in India next week, is not related to his key project of slashing the Department's budget, and is more to do with the fact Ivanka Trump is leading the US delegation this year. Trump was invited by Indian Prime Minister Narendra Modi in June, and this year's theme is supporting women entrepreneurs.

The State Department puts on the large yearly event, which Secretary of State John Kerry and even former President Barack Obama attended multiple times. But this year, according to one senior State Department official: "No one higher than the deputy assistant secretary is allowed to participate. The secretary and his top staff have insisted on approving all travel-- even the most minute details."

"They (Tillerson and his staff) won't send someone senior because they don't want to bolster Ivanka. It's now another rift between the White House and State at a time when Rex Tillerson doesn't need any more problems with the President," the official added.

A source close to the White House speaking on the condition of anonymity, said the thinner-than-past-years State Department delegation was absolutely being perceived and felt -- by several key people there -- as a snub, and that Tillerson's management style and extremely tight inner circle have rubbed some in the administration the wrong way.

Read More