AP Photo/Matt Rourke
Donald Trump listens to his mobile phone during a lunch stop in South Carolina.
Sharif apparently called Trump to congratulate him on winning the White House.
The Pakistani news release said Trump called Sharif a "terrific guy" with a "very good reputation."
"You are doing very good work which is visible in every way," Trump reportedly said to Sharif. "I am looking forward to see[ing] you soon."
He added, according to the readout of the call: "As I am talking to you, prime minister, I feel I am talking to a person I have known for so long."
Sharif and his family were caught amid a corruption scandal amid the release of the Panama Papers, and the embattled prime minister is currently facing increasing public uncertainty about his rule.
And this isn't Sharif's first go-around as prime minister of Pakistan - he was in power in the 1990s, but was eventually ousted in a military coup.
Trump also reportedly called Pakistan an "amazing" country with "tremendous opportunities."
"I am ready and willing to play any role that you want me to play to address and find solutions to the outstanding problems," Trump reportedly said. "It will be an honor and I will personally do it."
Sharif then reportedly asked Trump to visit Pakistan.
The news release said Trump said he "would love to come to a fantastic country, fantastic place of fantastic people."
Trump reportedly continued: "Please convey to the Pakistani people that they are amazing and all Pakistanis I have known are exceptional people."