Kushner also told US news site Axios that he did not mind the Palestinians do not trust him.
The Palestinians, he stated, "should have self-determination", without saying whether that would mean an independent state or some lesser form of autonomy.
Asked if the Palestinians could expect freedom from any Israeli regime or military interference, Kushner said "I think that it's a high bar".
The Palestinians have already dismissed the upcoming plan touted as the "deal of the century" by President Donald Trump, saying US actions so far have shown Washington is blatantly biased in favor of Israel.
The Washington Post said in April that the plan is likely to “stop short of ensuring a separate, fully sovereign Palestinian state.”
The so-called peace plan was expected to be unveiled at the end of the holy month of Ramadan in June.
During the interview, Kushner said he was not concerned over whether the Palestinians do not trust him.
"I'm not here to be trusted," he said, adding the Palestinian people would judge the deal based on whether "they think this will allow them to have a pathway to a better life or not."
Relations between the Palestinian Authority and the US took an unprecedented dip in late 2017, when Washington recognized Jerusalem al-Quds as Israel’s “capital”.
Palestinians want the West Bank as part of a future independent Palestinian state with East Jerusalem al-Quds as its capital. However, Israel insists on maintaining the occupation of Palestinian territories.
The Palestinians have rejected the US Middle East initiative as “the slap of the century” because it is said to hugely favor Israel.
Source: Press TV