There has likely been some back channel communications with the Kim regime, but I would be very surprised if President Trump was in direct contact with Kim Jong-un like he appears to be suggesting:
President Donald Trump suggested in an interview Thursday that he has developed a positive relationship with the North Korean leader, but declined to say whether they have spoken.
No sitting U.S. president is known to have spoken with a North Korean leader. The two nations have remained in a state of war and without diplomatic relations since the Korean War ended in 1953 without a peace treaty.
“I probably have a very good relationship with Kim Jong Un,” Trump told The Wall Street Journal. “I have relationships with people. I think you people are surprised.”
Asked if he had spoken with Kim, Trump was evasive: “I’m not saying I have or haven’t. I just don’t want to comment.” [Associated Press]
You can read more at the link.