Mr Trump made these remarks as PM Sharif called him to congratulate on his recent victory.
"I am ready and willing to play any role that you want me to play to address and find solutions to the outstanding problems. It will be an honour and I will personally do it. Feel free to call me any time, even before 20th January, that is before I assume my office," Mr Trump was quoted as saying in a statement released by Mr Sharif's office.
During the telephone conversation, Mr Trump also praised Mr Sharif and expressed his desire to meet the prime minister soon, Radio Pakistan reported.
In his reply, Mr Trump said he would love to visit the country and meet its people.
Earlier, Mr Trump had said that if elected, he'd like to mediate between India and Pakistan. But like the Obama administration, the US President-elect also said that he would only mediate if both countries asked him to do so.