"If we can get a working majority then we will come on January 31 at the absolute latest", Johnson told LBC radio.
The US President is due to arrive on Monday has cast Johnson as "Britain's Trump", and during a previous visit criticised Johnson's predecessor Theresa May over her Brexit policy.
U.S. President Donald Trump holds a bilateral meeting with British Prime Minister Boris Johnson (L) on the sidelines of the annual United Nations General Assembly in New York City, New York, U.S., September 24, 2019. The President expressed his condolences following the terrorist attack in London.
Pressed further, the official added: "He also, as I suspect you know, likes Boris Johnson - Prime Minister Johnson, personally".
However, Johnson said he would walk out of trade negotiations if including the health service was a pre-condition.
Corbyn has made post-Brexit transatlantic relations a key issue in his campaign, warning voters that the US will demand Britain's National Health Service be "on the table" in talks on a future trade deal.
How to Watch 49ers vs
Baltimore has fumbled 12 times but has only lost four, which is the fewest among the 26 teams who have fumbled 10 or more times . The San Francisco 49ers certainly appear capable of putting the brakes on Lamar Jackson and the high-powered Baltimore Ravens .
China angry as Trump backs Hong Kong bills
While Trump faced down Democrats in Washington, he also clashed with Chinese officials over what the administration called unfair trade practices.
Trump denies telling Giuliani to get Ukraine to investigate political foes
Giuliani give you a call and I am also going to have Attorney General Barr call and we will get to the bottom of it". Trump shrugged off the remarks when asked about them by a reporter Monday, calling Giuliani a "great guy".
The prime minister has denied this, and this week said if Washington tried to include the NHS in trade talks, "we'd walk away". They also objected to the overall prices Britain's NHS pays for USA pharmaceuticals.
At the other end of the political spectrum, Brexit Party leader Nigel Farage, a Trump ally and friend, is also hoping Trump's visit will benefit him and give a lift to his flagging electoral prospects.
But when Johnson struck his own exit deal, Trump questioned if it would allow a new trade agreement with the USA - something the prime minister has held up as one of the biggest prizes of Brexit.
As the election campaign enters its final weeks, Johnson told a press conference he wanted to keep in place preparations the government has made for the possibility of a no-deal Brexit.
The impeachment imbroglio has overshadowed Trump's presidency as he looks ahead to his own re-election fight next November.
Asked if he would rather be Prime Minister or have Britain leave the European Union, he replied: "I would rather get us out of the EU".