Saleem Altaf, the board's director of cricket operations, told Reuters he had met both players, who were recalled from the Champions Trophy in India on Monday after testing positive for the banned steroid nandrolone.
"They have said they don't ever recall taking this substance knowingly," Altaf said. "They have indicated they will press for another test when they appear before the drugs tribunal which will hear their case."
The players face a ban of one to two years under World Anti-Doping Agency (WADA) regulations. The International Cricket Council (ICC) has said that as Pakistan conducted the tests internally it should decide on their punishments.
Shoaib was accompanied to the meeting by his personal trainer and doctor, Tauseef Razzaq, who has said that the fast bowler could have taken nandrolone inadvertently while being treated with herbal medicine.
"After undergoing surgery in Australia earlier and subsequent treatment for the stress fracture, Shoaib has been seeing a hakim (doctor) in Pakistan. It is a possibility that nandrolone drug was mixed in herbal medicines that he has been taking," he said.
Altaf said the PCB would constitute the drugs tribunal by Friday. "We want to settle this matter as quickly as possible but in a fair manner."
Until the tribunal reached a decision the players remained suspended, he said.
"Obviously if they are found guilty their central contracts will be cancelled," he added.
Sources in the board told Reuters that Shoaib and Asif had meet Altaf separately for more than an hour and both looked worried.
Shoaib, 31, is one of the fastest bowlers in history. He has taken 165 Test wickets and more than 200 in one-dayers since his international debut in 1997.
He has been reported for a suspect bowling action three times and dogged by fitness problems for almost a decade.
Pakistan conducted the tests before the Champions Trophy, in which the ICC and WADA are carrying out random tests on two players from each of the 10 teams.
The ICC has allowed Pakistan to call up all rounder Yasir Arafat and spinner Abdul Rehman as replacements.
Pakistan won their opening match of the tournament on Tuesday against Sri Lanka.
