The two influential personalities are said to have been placed on the watch list over the alleged diversion of cash meant for arms into the 2015 election campaign and payment of huge ransom to unknown Boko Haram agents.
The EFCC also said it would not be intimidated or stampeded to release PDP's spokesman, Olisa Metuh.
The EFCC said since Metuh had refused to either refund the N400million traced to him or sign an undertaken to refund it, he will not be released.
Metuh will be allowed to go once he satisfies the condition for the discretion to be exercised in his favour, a top source told The Nation.
According to a top security source, Muazu and Tukur have been under investigation in the last few months on the arms cash disbursed for campaign purposes and counter-insurgency with Boko Haram.
The source said: “We need to interact with these two leaders, who are on watch-list. Since Muazu went for his daughter’s graduation and medical treatment, we have not been able to locate him.
“We learnt Muazu is around Singapore, Hong Kong and Malaysia axis. We are on his trail because some suspects have admitted drawing campaign funds from the ex-PDP national chairman. Over N600million has so far been traced to him.
"Tukur is believed to have been seen in the country by security agencies about three or four days ago. He might be invited over the botched deal with Boko Haram, which allegedly involved the payment of a ransom. He is also implicated in the disbursement of some funds for use in the Presidency for 2015 poll.”