At the White House during a Monday cabinet meeting, Trump said that issues in phase two of the deal would be, in many ways, a lot easier to work out than those in phase one.
He has said he would likely sign it when he met with Chinese President Xi Jinping at the Asia-Pacific Economic Cooperation summit, which will be held mid-November in Santiago.
World shares are mixed following upbeat talk by President Donald Trump and other USA officials on the status of trade negotiations with China.
On again, off again talks on resolving a dispute over trade and China's technology policies have dragged on for over a year, with both sides imposing billions of dollars' worth of tariffs on each other's goods.
"We would like to make a deal", Ross told Fox Business on Monday.
Last week Trump said he hopes that the first phase of the deal, announced earlier in October, will be signed by the middle of next month.
The comments from Kudlow and Ross come after Chinese Vice Premier Liu He said on Saturday that the two sides have made "substantial progress" in trade talks.
"We don't approve the tactic of brandishing the baton of tariffs at every turn and exerting maximum pressure on China", said China's Vice Minister of Foreign Affairs Le Yucheng.
Commerce Secretary Wilbur Ross was more cautious, saying that the timing was less important than the contents of any deal.