"I really believe that we have a very good chance of getting the taxes done ... hopefully fairly long before the end of the year," the president said in a hastily scheduled, roughly 40-minute news conference following a lunch with the Kentucky Republican.
McConnell added: "The goal is to get it done by the end of the year."
The GOP faces multiple hurdles in meeting the target for approving a tax plan. Tax-writing committees have not yet crafted a bill, while lawmakers have other legislative deadlines to meet before the end of the year, as well.
Last week, Sen. Ted Cruz told CNBC that passing a tax bill may not happen until next year.
McConnell said the Senate still needs to pass a fiscal 2018 budget resolution, then approve a joint budget with the House, before a more concrete plan takes shape. The chamber hopes to pass it this week.
Passing a budget proposal allows Republican senators to use rules in which the GOP can pass a bill with only Republicans votes in the Senate.
Trump said he wants to see "minor adjustments" to the framework unveiled by Republicans to "make sure that the middle class is the biggest beneficiary." He did not specify what those changes would be.
The tax framework released last month calls to slash rates broadly for individuals and businesses while raising the standard deduction and getting rid of other deductions. It lacked clear provisions to offset the revenue lost by the cuts.
The budget deficits generated by the potential plan, as well as a proposal to get rid of state and local tax deductions, have also emerged as sticking points for Republicans.
Trump and McConnell aimed to put on a united front and said they have the same policy goals. The president has publicly chided McConnell several times, including tweets berating him for failing to pass an Obamacare repeal bill in the Senate.
In August, The New York Times reported that a phone call between the pair "quickly devolved into a profane shouting match."
Still, the president said he has an "outstanding" relationship with McConnell. The senator concurred.
"Contrary to what some of you may have reported, we are together totally on this agenda to move America forward," McConnell said.
The president said that extends to other Republicans in Congress.
"If you read the papers, you think it's like I am on one island and they're like on the other. Well, it is not the way it is. We have a fantastic relationship," Trump said. "I am friends with most of them, I can say. I don't think anybody could have much of a higher percentage. But I am friends of most of them. I like and respect most of them and I think they like and respect me."
One top Republican in particular — Sen. Bob Corker of Tennessee — has publicly ribbed Trump, telling the Times that the president is leading the United States on the path to World War III. Corker, who is not running for re-election next year, suggested many of his colleagues privately agree with him.