"I have asked him what he would think of this one and that one," Trump told NBC's Matt Lauer on "The Today Show."
"I take his recommendations very seriously," Trump added. "And there are some people that I will be appointing and, in one case, have appointed where he thought very highly of that person."
There have been "at least a handful" of conversations between the President and Trump, White House Press Secretary Josh Earnest said Wednesday, although he declined to characterize in any detail the content of the discussions.
"The President is responsive to requests and phone calls from the President-elect," Earnest said.
"He's certainly pleased that he can offer advice and assistance that may be useful to the incoming administration," he added.
Trump said he has talked to Obama about his perspective on the greatest challenges facing America.
"I've asked him what he thinks are the biggest problems, greatest assets," Trump said in the interview with Lauer, which was focused on Trump being named on Wednesday as Time's "Person of the Year." "We have very good dialogue."
On Tuesday, Joe Biden praised some of Trump's Cabinet selections, calling them "very solid" while expressing concerns about others.
"If you look at the people that Donald Trump has named so far, some give me great pause. There's other people he's appointed in the administration that are very solid," Biden said on "The Late Show" with Stephen Colbert. "So it's just -- I don't think anybody knows for certain, but we have to be vigilant, and when in fact it looks like the administration is moving in the direction that is harmful or dangerous."
During the final stretch of the campaign, the back-and-forth attacks and jabs between Trump and Obama were among the harshest seen between a sitting president and the nominee of his rival party.
Obama regularly hit the campaign trail mocking Trump's inexperience in policy-making and fondness for tweeting controversial things. And the businessman regularly called Obama a weak leader in the fight against terrorism.
But Trump, who visited the White House and met with Obama after the election, said Wednesday that he actually "really likes" the President.
"I must tell you, you know, I never met him before this. I never spoke to him before this. I really -- I do like him," Trump said. "I love getting his ideas. And I may differ in many cases. I differ very greatly."
Asked if Obama liked Trump just as Trump declared this morning that he liked Obama, Earnest told CNN's Michelle Kosinski, "For the president's personal feelings you should talk to the president about that. I can't speak to their personal relationship."
Trump spent years challenging Obama's birthplace and whether he was eligible to serve as President, and he also vowed during the campaign to "repeal and replace" the President's signature accomplishment, Obamacare.
While Trump has been quickly filling high-profile positions in his upcoming Cabinet, the choice for Secretary of State has attracted the most attention in part because Trump is considering nominating Mitt Romney, one of his harshest critics during the campaign.
"I've spoken to him a lot," Trump said of Romney. "We've come a long way together. We had some tremendous difficulty together and now I think we've come a long way."
Trump, who said he may announce his pick for the nation's top diplomate next week, dismissed speculation that he is just stringing Romney along to embarrass the former 2012 Republican presidential candidate.
"No, it's not about revenge. It's about what's good for the country. I'm able to put this stuff behind us," Trump said. "I hit him very hard also, which is very nice that the press doesn't cover that. I'm very happy about that actually."
Obama first welcomed Trump to the White House days after the Republican was elected - just days after the President had called Trump unfit to control the nuclear launch codes.
The meeting was the beginning of a bit of a softening between the two with Obama telling his successor that he wanted him to succeed and adding that he would do everything he could to ensure a smooth transition.
"Mr. President, it was a great honor being with you and I look forward to being with you many, many more times," Trump said following their 90-minute meeting.