While it was good news that Mr Trump spoke to Mr Sharif, the chat will do no favour to the premier in the Panamagate case, the Tehreek-i-Insaf Chairman tweeted.
Mr Khan was referring to Mr Sharif's telephonic conversation with Mr Trump yesterday, during which the Pakistani premier congratulated America's president-elect on his recent victory in the US polls.
Mr Trump told Prime Minister Sharif that he has a "very good reputation".
In a taunting reference to a letter by Qatari prince Sheikh Hamad bin Jassim bin Jaber Al-Thani, Mr Khan said Mr Sharif could not be saved from the Panama Papers scandal "even if a Trump letter arrived", Dawn reported.
In the letter, the Qatari royal had described his father's business ties with Sharif's family and his involvement in the London apartments that are at the centre of the Panama Papers controversy.
Mr Khan on November 14 submitted the documents containing details of alleged bank accounts held by the Sharif family and loan write-off schemes.