Gilani is upset with several key aides of the President, including Malik, for bypassing him and other members of the ministry, media reports said in Islamabad.
He has said that Malik's recent announcement about authorities clamping down on 'anti-government' emails and SMS messages will not be implemented.
Gilani also said that nobody will be allowed to make such announcements in future without consulting the cabinet. A media report on Wednesday also claimed that Malik may be eased out soon and replaced by senior Pakistan People's Party leader Raza Rabbani.
Pakistani media has been reporting on differences between Gilani and Zardari on several key issues, though the Prime Minister has sought to dispel any such impression in public.
Gilani, the reports said, is "now in an aggressive mood" and "very confident after emerging victorious from Sharm-el-Sheikh."
Gilani earned praise in Islamabad for bringing up the issue of alleged 'Indian interference' in the restive Balochistan province during his July 16 meeting with Prime Minister Manmohan Singh on the sidelines of the Non-Aligned Movement summit in Sharm el-Sheikh, Egypt.
